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The job sequencing and tool switching (SSP) is a well-known combinatorial optimization problem that aims to minimize the number of tool switches. The problem mainly arises in a flexible manufacturing system, in which machines can be configured with various tools to process different jobs and tool switches will correspond to a reduction of productivity. While the general studies assume uniform setup time for tool switching, applications on the industries indicate that the setup time of a tool might depend on the previously installed tool of the same slot. Therefore, this article proposes two integer linear programming models for the sequence-dependent SSP, namely the five-index formulation and the multicommodity flow formulation. Experimental tests are executed to compare the sequence-dependent SSP with the uniform SSP and the results show the effectiveness of multicommodity flow formulation. Finally, several managerial discussions are derived from the results.

Introducing InterSatellite Links (ISLs) is a major trend in new-generation Global Navigation Satellite Systems (GNSSs). Data transmission scheduling is a crucial problem in the study of ISL management. The existing research on intersatellite data transmission has not considered the capacities of ISL bandwidth. Thus, the current study is the first to describe the intersatellite data transmission scheduling problem with capacity restrictions in GNSSs. A model conversion strategy is designed to model the aforementioned problem as a length-bounded single-path multicommodity flow problem. An integer programming model is constructed to minimize the maximal sum of flows on each intersatellite edge; this minimization is equivalent to minimizing the maximal occupied ISL bandwidth. An iterated tree search algorithm is proposed to resolve the problem, and two ranking rules are designed to guide the search. Experiments based on the BeiDou satellite constellation are designed, and results demonstrate the effectiveness of the proposed model and algorithm.

Bus driver rostering generates the work plan for a pool of drivers during a planning period of predefined length. This plan, called the roster, must consider the balance between the pressure of costs, the provision of a service of high quality, labour agreements, and the goodwill of the workers. The bus driver rerostering problem occurs during real-time operational planning, when unexpected events—such as non-planned absences of drivers—disrupt the roster. To reconstruct a roster which is originally built in a context of days off schedules for drivers, we propose a reactive methodology based on a multicommodity flow assignment mixed integer linear programming model. The objective is to minimise the number of depot drivers who are assigned to drive and the number of postponed days off, as well as the dissimilarity between the reconstructed and the original roster and the balancing of the workload. The proposed algorithm enables the disrupted roster to be reconstructed at the expense of a relatively small number of changes in drivers’ work and rest periods, while, at the same time, controlling the dimension of the multicommodity flow network. Computational experience based on real-life based instances revealed that the algorithm has the ability to produce reconstructed rosters with few changes to the drivers’ original work assignment, in a short CPU time.

Origin-destination integer multicommodity flow problems differ from classic multicommodity models in that each commodity has one source and one sink, and each commodity must be routed along a single path. A new invisible-hand heuristic that mimics economic markets' behavior is presented and tested on large-scale telecommunications networks, with solution times two orders of magnitude faster than Cplex's LP relaxation, more dramatic MIP ratios, and small solution value differences.

Pin accessibility encounters nontrivial challenges due to the smaller number of routing tracks, higher pin density, and more complex design rules. Consequently, securing design rule-correct routability has become a critical bottleneck for sub-10-nm IC designs (particularly in the detailed routing stage) costing days of runtime. To reduce turnaround time, IC designers demand new design methodologies to analyze the routing feasibility of a given layout architecture (e.g., conditional design rules, pin assignment patterns, etc). There are several conventional methods capable of assessing routability that consider pin accessibility. However, precise diagnosis of unroutable layouts remains an open problem for IC design practitioners. In this article, we propose two novel frameworks that: 1) efficiently analyzes design rule-correct routability via an integer linear programming (ILP)-derived Boolean satisfiability (SAT) formulation written in light-weight conjunctive normal form, on top of multicommodity flow theory and 2) precisely diagnose explicit reasons for design-rule violations (DRVs) in the form of human-interpretable explanations, while specifying conflicting design rules with a physical location. While covering a variety of conditional design rules, we have refined our formulation by using SAT encoding techniques, supernode simplification, Boolean constraint propagation-based preprocessing, etc. We demonstrate that our routability analysis framework produces design rule-correct routability assessment within 0.02% of ILP runtime on average. Also, our routability diagnosis framework precisely examines DRVs, revealing design-rule conflicts for a variety of pin layouts and switchboxes. We show our frameworks scalability by utilizing practical benchmarks ranging up to 40 000 grid-size layouts (i.e., 200 Htrack $\times $ 200 Vtrack), producing results within an hour.

In this work , one proposes a model to evaluate the optimal deployment of Centralised Radio Access Network (C- RAN ) architecture elements , i.e. Base Band processing Units ( BBUs ) and fronthaul links , in a brown- field scenario, in which traditional base stations are already deployed and a physical network is present. The proposed optimisation framework jointly optimises BBU placement and access network infrastructures deployment . It clusterises the Remote Radio Heads in the scenario through a Multicommodity Flow approach , and solves the minimum cost fronthaul network deployment through a Rooted Delay - Constrained Minimum Spanning Tree approach . Optical fibre and microwave links are considered as fronthaul infrastructures . The proposed optimisation framework is validated through a comparison with a theoretical output for a canonical scenario, being afterwards applied to a real scenario. A cost analysis for different scenario configurations is presented , and trade - offs and guidelines for a cost optimal deployment of C- RAN are provided . The analysis of results for the real scenario of the city of Lisbon and its surrounding areas shows that the delay budget in the fronthaul network highly impacts on capital expenditures as well as on operational ones . It is shown that a larger delay budget enables an annual cost reduction up to 72 % in urban areas and 54 % in rural ones .

The switch Markov chain has been extensively studied as the most natural Markov chain Monte Carlo approach for sampling graphs with prescribed degree sequences. We show that the switch chain for sampling simple undirected graphs with a given degree sequence is rapidly mixing when the degree sequence is so-called strongly stable. Strong stability is satisfied by all degree sequences for which the switch chain was known to be rapidly mixing based on Sinclair's multicommodity flow method up until a recent manuscript of Erdős and coworkers in 2019. Our approach relies on an embedding argument, involving a Markov chain defined by Jerrum and Sinclair in 1990. This results in a much shorter proof that unifies (almost) all the rapid mixing results for the switch chain in the literature, and extends them up to sharp characterizations of P-stable degree sequences. In particular, our work resolves an open problem posed by Greenhill and Sfragara in 2017.

The maritime industry is one of the greenest modes of transportation, taking care of almost 90% of the global trade. The maritime container business revolves around liner shipping, which consists of container vessels sailing on fixed itineraries. For the last 20 years, there has been an increasing number of publications regarding how to design such fixed routes (services), to ensure a high level of service while minimizing operational costs and environmental impact. The liner shipping network design problem can briefly be described as follows: Given a set of demands (defined by origin, destination, time limit) and a set of vessels with variable capacity, the task is to design a set of weekly services, assign vessels to the services, and flow the demand through the resulting network such that it arrives within the stated time constraints. The objective is to maximize revenue of transported demand subtracting the operational costs. We present an in-depth literature overview of existing models and solution methods for liner shipping network design, and discuss the four main families of solution methods: integrated mixed integer programming models; two-stage algorithms designing services in the first step and flowing containers in the second step; two-stage algorithms first flowing containers and then designing services; and finally algorithms for selecting a subset of proposed candidate services. We end the presentation by comparing the performance of leading algorithms using the public LINER-LIB instances. The paper is concluded by discussing future trends in liner shipping, indicating directions for future research.

Robust multiperson tracking requires the correct associations of online detection responses with existing trajectories. In this paper, we propose to integrate multiple cues to resolve the ambiguities in data association for multiperson tracking. Unlike most existing algorithms which integrate multiple cues in the same manner for different scenes, we learn scene-specific parameters to integrate multiple cues for different scenes, as the discriminative power of each cue may vary in different scenes. The scene-specific integration parameters are learned offline by supervised learning method. Min-cost multicommodity flow is employed to solve the data association task. The edge cost of the multicommodity network, which is crucial for the data association, is determined by integrating the multiple cues extracted from the detection response based on the learned scene-specific integration parameters. The experimental results on public multiperson tracking data set demonstrate the effectiveness of the proposed scene-specific integration method.

In this paper a new multicommodity flow mathematical model for the Job Sequencing and Tool Switching Problem (SSP) is presented. The proposed model has an LP relaxation lower bound equal to the num...

This paper deals with multi-depot bus scheduling (MDBS) problem. Depot workload balancing constraints are introduced. In this case, the problem can be stated as a two-objective multi-commodity flow...

This article discusses the guide path design of automated guided vehicle (AGV) systems for which we propose a model that incorporates a dynamic multicommodity flow with capacity constraints from a pickup to a delivery point. The problem is formulated as the selection of a guide path connecting a given set of pickup/delivery points. A cell-based local search that is based on an original neighborhood technique is developed. In the proposed method, the guide path is effectively optimized based on a local search of cell-based neighborhood search preserving connectivity constraints and the subsequent solution of a dynamic multicommodity flow problem. The performance of the proposed method is strengthened by the redundant elimination of arcs and intensification of search according to the concept of the flow-concentrated cell. The effectiveness of the proposed method is demonstrated by comparing it with a general-purpose solver and recent algorithms for fixed-charge capacitated multicommodity network design problems. A real case study is presented to demonstrate the applicability of the proposed method by using simulation software. Note to Practitioners —Due to the recent growth of online shipping, the design of automated warehousing systems is receiving much attention. Most automated warehousing systems introduce multiple automated guided vehicles (AGVs) for transportation. This article presents an efficient optimization of guide path design considering congestions and dynamic multicommodity flow routing. We develop cell-based local search heuristics for the guide path design problem for AGV systems that can be applied to a large-scale transportation model to solve the problem efficiently. Our major finding is that the guide path design with the dynamic multicommodity flow can significantly reduce the delays caused by congestions and improve the efficiency of the warehousing systems. The effectiveness of the derived guide path design is evaluated by simulation software. The feasibility of the guide path is confirmed in several case studies.

We consider the problem of optimizing the achievable EPR-pair distribution rate between multiple source-destination pairs in a quantum Internet, where the repeaters may perform a probabilistic Bell-state measurement and we may impose a minimum end-to-end fidelity as a requirement. We construct an efficient linear programming (LP) formulation that computes the maximum total achievable entanglement distribution rate, satisfying the end-to-end fidelity constraint in polynomial time (in the number of nodes in the network). Our LP formulation gives the optimal rate for a class of entanglement generation protocols where the repeaters have very short-lived quantum memories. We also propose an efficient algorithm that takes the output of the LP solver as an input and runs in polynomial time (in the number of nodes) to produce the set of paths to be used to achieve the entanglement distribution rate. Moreover, we point out a practical entanglement generation protocol that can achieve those rates.

Time-varying network flows (also called dynamic network flows) generalize standard network flows by introducing an element of time. In this paper, we consider the dynamic version of the minimum cost multicommodity flow problem with storage at intermediate nodes. This problem is known to be NP-hard. By using of the flow decomposition theorem in network flows, we propose an efficient model based on dynamic path flows for this problem. For some special structures of the path-flow formulation, we provide an algorithm based on decomposition principle, for solving the proposed model. In the end, the efficiency of the proposed approach is evaluated through a number of experimental tests.

Within the formalism of the mathematical model of transferring a multicommodity flow, the reachability set of multiuser network systems is studied. A method is proposed for constructing an internal supporting frame based on the vectors of the maximum flows that can be transferred between all pairs of nodes in exclusive and limited exclusive modes of flow control. Using the obtained limit values, we construct a polyhedron of a simpler structure (frame) belonging to the set of reachable multi-flows and a cone of possible directions for the generation of boundary points. Methods for obtaining various multicriteria evaluations of the functional capabilities of a transmission network are considered. The developed approach can be used for the a priori analysis of the set of reachable multiflows, including quickly obtaining estimates and acceptable options for the fair distribution of the limited capacity of the transmission network.

The analysis of network routing games typically assumes precise, detailed information about the latency functions. Such information may, however, be unavailable or difficult to obtain. Moreover, one is often primarily interested in enforcing a desired target flow as an equilibrium. We ask whether one can achieve target flows as equilibria without knowing the underlying latency functions. We give a crisp positive answer to this question. We show that one can efficiently compute edge tolls that induce a given target multicommodity flow in a nonatomic routing game using a polynomial number of queries to an oracle that takes tolls as input and outputs the resulting equilibrium flow. This result is obtained via a novel application of the ellipsoid method, and extends to various other settings. We obtain improved query-complexity bounds for series-parallel networks, and single-commodity routing games with linear latency functions. Our techniques provide new insights into network routing games.

Within the formalism of the multicommodity flow model, changes in the functional characteristics of a multiuser network after a damage are studied. To analyze the original limiting capabilities of the system, the maximum flow is calculated for each pair of vertices independently of other pairs. All edges of the corresponding minimum cut are removed, and the maximum possible flows for all origin–destination pairs are found in the damaged network and compared with their initial values. The detriment is evaluated for various cuts (structural damages). The influence of structural damages on the attainable values of the flow for each pair of vertices is investigated. This makes it possible to rank the origin–destination pairs by their susceptibility to the influence of damages from a given class. Ranking is performed on the basis of a bi-criteria detriment evaluation model. This approach is used for analyzing the vulnerability of large territory distributed systems, including telecommunication systems, communication and control systems.

This article addresses a variant of the Discrete Cost Multicommodity Flow (DCMF) problem with random demands, where a penalty is incurred for each unrouted demand. The problem requires finding a network topology that minimizes the sum of the fixed installation facility costs and the expected penalties of unmet multicommodity demands. A two-stage stochastic programming with recourse model is proposed. A simulation-optimization approach is developed to solve this challenging problem approximately. To be precise, the first-stage problem requires solving a specific multi-facility network design problem using an exact enhanced cut-generation procedure coupled with a column generation algorithm. The second-stage problem aims at computing the expected penalty using a Monte Carlo simulation procedure together with a hedging strategy. To assess the empirical performance of the proposed approach, a Sample Average Approximation (SAA) procedure is developed to derive valid lower bounds. Results of extensive computational experiments attest to the efficacy of the proposed approach. Scopus

We consider a problem arising in the design of ad-hoc wireless sensor networks. Given a connected bidirectional digraph with n sensors and a fixed sink, the p-arborescence star problem is the problem of clustering the sensors into p disjoint subsets and defining a directed backbone that spans the sink and all p cluster-heads, one for each cluster. The overall objective of the problem is to minimize the sum of intra and inter-cluster costs. We introduce and compare formulations based on directed cutset constraints and multicommodity flow variables. Valid inequalities to strengthen the models are also given. To solve these models, we develop efficient cutting-plane methods. We carry out extensive computational experiments and comparisons to illustrate the performance of our methods.

Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network in which vertices express their preferences over their incident edges. A network flow is stable if there is no group of vertices that all could benefit from rerouting the flow along a walk. Fleiner (Algorithms 7:1–14, 2014) established that a stable flow always exists by reducing it to the stable allocation problem. We present an augmenting path algorithm for computing a stable flow, the first algorithm that achieves polynomial running time for this problem without using stable allocations as a black-box subroutine. We further consider the problem of finding a stable flow such that the flow value on every edge is within a given interval. For this problem, we present an elegant graph transformation and based on this, we devise a simple and fast algorithm, which also can be used to find a solution to the stable marriage problem with forced and forbidden edges. Finally, we study the stable multicommodity flow model introduced by Kiraly and Pap (Algorithms 6:161–168, 2013). The original model is highly involved and allows for commodity-dependent preference lists at the vertices and commodity-specific edge capacities. We present several graph-based reductions that show equivalence to a significantly simpler model. We further show that it is $${\textsf {NP}}$$ -complete to decide whether an integral solution exists.

The paper presents a comparison between three approaches to solving the length-bounded maximum multicommodity flow problem with unit edge-lengths. Following the first approach, Garg and K?nemann?s, we developed an improved fully polynomial time approximation scheme for this problem. As the second alternative, we considered the well-known greedy approach. The third approach is the one that yields exact solutions by means of a standard LP solver applied to an LP model on the time-expanded network. Computational experiments are carried out on benchmark graphs and the graphs that model software defined satellite networks, to compare the proposed algorithms with an exact linear programming solver. The results of the experiments demonstrate a trade-off between the computing time and the precision of algorithms under consideration.

We derive an analytical expression for the mean load at each node of an arbitrary undirected graph for the non-uniform multicommodity flow problem under weighted random routing. We show the mean load at each node, net of its demand and normalized by its (weighted) degree, is a constant equal to the trace of the product of two matrices: the Laplacian of the demand matrix and the generalized inverse of the graph Laplacian. For the case of uniform demand, this constant reduces to the sum of the inverses of the non-zero eigenvalues of the graph Laplacian. We note that such a closed-form expression for the network capacity for the general multicommodity network flow problem has not been reported before, and even though (weighted) random routing is not a practical procedure, it enables us to derive a (tight) upper bound for the capacity of the network under more standard routing policies. Using this new expression, we compute network capacity for a sample of demand matrices for some prototypical networks, including uniform demand (one unit between all node pairs) and broadcast demand (one unit between a source node and each other node as destination), and finally derive estimates of the mean load in some asymptotic cases.

This chapter presents a new mathematical formulation, which is based on multicommodity flow, for a classical capacitated minimum spanning tree problem. It also demonstrates the performance of Van Roy’s cross decomposition algorithm for solving the capacitated minimum spanning tree can be significantly improved by incorporating an edge exchange heuristic algorithm at a tremendous saving in the computational effort. The results also reveal that the proposed algorithm is very competitive with Lagrangian original algorithm in terms of solution quality. The use of the new formulation and the proposed algorithm which take better advantage of the problem structure, especially that of the dual subproblem, provide a large potential for improvement.

We deal with a problem which combines storage location assignment with sequencing decisions about the assigned storage locations. Given a set of different product types, with the corresponding storage demand, a set of capacitated storage locations has to be assigned to each product type for the corresponding storing operations. In addition, a suitable sequencing of the assigned storage locations must be devised for each product type, i.e., it has to be decided the ordering with which the storage locations will be filled up during the storing operations. A motivation is that a First-In First-Out (FIFO) picking criterion among storage locations is required per product type. The sequencing established for the assigned storage locations will therefore allow to easily implement the FIFO policy in the successive order picking. Moreover, the selected sequencing also determines the availability of extra storage per product type, on top of pairs of consecutive storage locations along the sequence. The goal is to maximize the storage capacity which remains available after the assignment of the storage locations. We prove the NP-Hardness of the problem and we model it as a constrained multicommodity flow problem on an auxiliary graph. We then propose a Mixed-Integer Linear Programming (MILP) model, with some valid inequalities, based on the multicommodity flow formulation. Two relaxations are proposed as well to estimate the quality of the model solutions. Two matheuristic approaches are then designed starting from the MILP model. The proposed methodology is applied to a case study related to a large warehouse with a high stock rotation index in tissue logistics, which motivated our study. Computational results on a wide test bed related to such a real application context show the efficiency and the efficacy of the presented approaches.

The multicommodity flow problem deals with the transshipment of more than one commodity from respective sources to corresponding sinks without violating the capacity constraints. Due to the capacity constraints, flows out from the sources may not reach their sinks, and so, the storage of excess flows at intermediate nodes plays an important role in the maximization of flow values. In this paper, we introduce the maximum static as well as maximum dynamic multicommodity flow problems with intermediate storage. We present polynomial and pseudopolynomial time algorithms for the former and latter problems, respectively. We also present the solution procedures to these problems in contraflow network having symmetric as well as asymmetric arc transit times. We transform the solutions in continuous-time settings by using natural transformation.

In this paper we derive an analytical expression for the mean load at each node of an arbitrary undirected graph for the uniform multicommodity flow problem under random walk routing. We show the mean load is linearly dependent on the nodal degree with a common multiplier equal to the sum of the inverses of the non-zero eigenvalues of the graph Laplacian. Even though some aspects of the mean load value, such as linear dependence on the nodal degree, are intuitive and may be derived from the equilibrium distribution of the random walk on the undirected graph, the exact expression for the mean load in terms of the full spectrum of the graph has not been known before. Using the explicit expression for the mean load, we give asymptotic estimates for the load on a variety of graphs whose spectral density are well known. We conclude with numerical computation of the mean load for other well-known graphs without known spectral densities.

Virtual Network Embedding (VNE) that addresses the embedding problems of heterogeneous virtual networks onto a physical limited-capacity infrastructure efficiently is a major challenge in network virtualization (NV). VNE is computationally intractable when considering various constraints on nodes and links, and is also known as ${\mathcal{N}}{\mathcal{P}}$-hard even in offline embedding. Although the VNE problems have received attentions over recent decades with a vast number of VNE solutions, the majority of them only focus on VNE node mapping, whilst leaving the link mapping stage for the shortest path method or multicommodity flow (MCF) algorithm. We persuasively argue that node and link mappings equally play pivotal roles to approach an efficient VNE solution. In this paper, we reassess the role of link mapping stage in VNE problem, and then propose a novel intelligent VNE orchestration which effectively implements a distributed parallel model to reduce the operation time remarkably. Extensive evaluation results show that our proposed algorithm is not only faster than state-of-the-art VNE algorithms in speed, but also better in all performance metrics.

Reliable operation, test, debug and diagnosis of complex integrated systems are ensured by embedded instruments, such as sensors, aging monitors or Built-In Self-Test (BIST) registers. Reconfigurable Scan Networks (RSNs) offer a flexible and efficient way to access such test instruments throughout the whole life-cycle. However, improper RSN integration might introduce additional connectivity properties to the device under test (DUT), which can be exploited to perform unauthorized access or cause information leakage. The existence of such additional connectivity through the RSN can compromise the security of the DUT and is considered as a security threat.In this paper, a method is presented to resolve all such security compliance violations. The problem is formulated in terms of Integer Linear Programming (ILP) as a minimum cut problem in multicommodity flow. An efficient heuristic is presented, which, to our knowledge, for the first time allows to consider the whole set of violations simultaneously and thereby to find a minimized number of changes to the RSN structure in order to make it compliant with the initial security requirements of the DUT and prevent the information leakage through the scan chain.

In this paper, we bound the integrality gap and the approximation ratio for maximum plane multiflow problems and deduce bounds on the flow-cut-gap. Planarity means here that the union of the supply and demand graph is planar. We first prove that there exists a multiflow of value at least half of the capacity of a minimum multicut. We then show how to convert any multiflow into a half-integer one of value at least half of the original multiflow. Finally, we round any half-integer multiflow into an integer multiflow, losing again at most half of the value, in polynomial time, achieving a $1/4$-approximation algorithm for maximum integer multiflows in the plane, and an integer-flow-cut gap of $8$.

The maximum concurrent flow problem (MCFP) is a multicommodity flow problem in which every pair of vertices can send and receive flow concurrently. The objective of MCFP is to find a maximum throughput and the flow corresponding to the throughput under a set of capacity constraints. We present an improved version of the Flow Deviation Method for the maximum concurrent flow problem, which was first presented by Daniel Bienstock and Olga Raskina in 2000. The algorithm is based on linear programming formulation involving Frank-Wolfe procedure and minimum-cost flow problem. The correctness of the algorithm is strictly proved and the performance is evaluated under several networks of different sizes.

The multicommodity flow problem arises when several different commodities are transshipped from specific supply nodes to the corresponding demand nodes through the arcs of an underlying capacity network. The maximum flow over time problem concerns to maximize the sum of commodity flows in a given time horizon. It becomes the earliest arrival flow problem if it maximizes the flow at each time step. The earliest arrival transshipment problem is the one that satisfies specified supplies and demands. These flow over time problems are computationally hard. By reverting the orientation of lanes towards the demand nodes, the outbound lane capacities can be increased. We introduce a partial lane reversal approach in the class of multicommodity flow problems. Moreover, a polynomial-time algorithm for the maximum static flow problem and pseudopolynomial algorithms for the earliest arrival transshipment and maximum dynamic flow problems are presented. Also, an approximation solution to the latter problem is obtained in polynomial-time.

Designing and optimizing different flows in networks is a relevant problem in many contexts. While a number of methods have been proposed in the physics and optimal transport literature for the one-commodity case, we lack similar results for the multi-commodity scenario. In this paper we present a model based on optimal transport theory for finding optimal multi-commodity flow configurations on networks. This model introduces a dynamics that regulates the edge conductivities to achieve, at infinite times, a minimum of a Lyapunov functional given by the sum of a convex transport cost and a concave infrastructure cost. We show that the long time asymptotics of this dynamics are the solutions of a standard constrained optimization problem that generalizes the one-commodity framework. Our results provide new insights into the nature and properties of optimal network topologies. In particular, they show that loops can arise as a consequence of distinguishing different flow types, complementing previous results where loops, in the one-commodity case, were obtained as a consequence of imposing dynamical rules to the sources and sinks or when enforcing robustness to damage. Finally, we provide an efficient implementation of our model which convergences faster than standard optimization methods based on gradient descent., Comment: 13 pages, 7 figures

Video streaming services employ the Internet to distribute content to an ever-increasing number of concurrent viewers. The delivery architecture employed by leading video platforms requires players to run a control algorithm dynamically choosing the video bitrate to match the time-varying network bandwidth and avoid playback interruptions due to buffer underruns. Such an algorithm is generally designed to (selfishly) improve the quality individually perceived by users. Consequently, this control architecture leads, in the optimal case, to maximize the average quality perceived collectively by all users and not to a distribution of resources that is fair in terms of user perceived quality. We argue that video service providers should manage their delivery network to address fairness issues to gracefully degrade the perceived quality equally for all users when resources become scarce. Even though the general problem of providing a fair level of perceived quality does not scale with the cumbersome number of concurrent users, this paper shows that the Multi-Commodity Flow Problem (MCFP) optimization framework is a proper and efficient tool to address this open issue. First, we show how to cast the resource allocation problem to an MCFP and then we propose a strategy to make the resulting problem tractable for video distribution platforms serving massive audiences. The performance of the proposed optimal fair resource allocation strategy is assessed using realistic simulations involving thousands of concurrent video sessions on a real network topology by varying both the total load on the network and key system parameters.

The Minimum Cost Hop-and-root Constrained Forest Problem (MCHCFP) is a combinatorial optimization problem that arises in the design of energy efficient wireless sensor networks with mobile sinks. It aims at providing a communication topology that minimizes energy consumption while controlling network latency and message loss due to communication failure. The problem is defined in terms of a mixed graph G = ( V , E , A ) with set of vertices V (representing the sensor nodes), edges E, arcs A, and parameters K , H ∈ N , and D ∈ R + . Each edge has an associated length, and each arc has an associated cost. The MCHCFP aims at finding a rooted spanning forest of (V, A) with minimum total cost. The solution must be hop constrained, in the sense that the path from any leaf to its root in the forest does not have more than H arcs, as well as distance constrained, so that one must be able to find K routes of length at most D, visiting exactly once the chosen roots of the forest. We study four integer programming formulations, two of them are new, the other two come from the literature. The first formulation coming from the literature is a multicommodity flow based model. The second is a Dantzig–Wolfe reformulation of the first. The two new formulations, which are equivalent with respect to their linear programming bounds, arise when the problem is formulated over a layered graph. To evaluate the bounds implied by the formulations other than the network flow model, we develop algorithms based on delayed column and/or row generation. We provide computational experiments showing that the best lower bounds are given by the formulations based on the layered graph. The reformulation coming from the literature provides lower bounds that are very close to those provided by the layered graph formulations, but in significantly less computational time. As it provides the best trade-off between lower bound quality and computational effort, that reformulation is thus chosen as the basis for a branch-and-price algorithm introduced here. Such an algorithm managed to solve instances with up to 60 vertices, a significant improvement over the previous approach in the literature, which systematically solves instances with up to 20 vertices.

Telecommunication networks can be seen as the stacking of several layers like, for instance, IP-over-Optical networks. This infrastructure should have sufficient capacities to route some demands between their origin-destination nodes. In this paper we consider the Capacitated Multi-Failure Survivable Network Design problem. We study two variants of this problem with simple and multiple capacities. We give two multicommodity flow formulations for each variant of this problem and describe some valid inequalities. In particular, we characterize valid inequalities obtained using Chvatal-Gomory procedure from the well known Cutset inequalities. We show that some of these inequalities are facet defining. We discuss separation routines for all the valid inequalities. Using these results, we develop a Branch-and-Cut algorithm and a Branch-and-Cut-and-Price algorithm for each variant and present extensive computational results.