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This study focuses on the load balancing of the transactions in the blockchain. The problem is how to assign these transactions to the blocks. The objective is to guarantee a load balancing of the workload in the time of blocks. The proposed problem is an NP-hard one. To face the hardness of the studied problem, the challenge is to develop algorithms that solve the problem approximately. Finding an approximate solution is a real challenge. In this paper, nine algorithms are proposed. These algorithms are based on the dispatching-rules method, randomization approach, clustering algorithms, and iterative method. The proposed algorithms return approximate solutions in a remarkable time. In addition, in this paper, a novel architecture composed of blocks is proposed. This architecture adds the component "Balancer". This component is responsible to call the best-proposed algorithm and solve the scheduling problem in a polynomial time. In addition, the proposed work helps users to solve the problem of big data concurrency. These algorithms are coded and compared. The performance of these algorithms is tested over three classes of instances. These classes are generated based on uniform distribution. The total number of instances tested is 1350. The average gap, execution time, and the percentage of the best-reached value are used as metrics to measure the performance of the proposed algorithms. Experimental results show the performance of these algorithms and a comparison between them is discussed. The experimental results show that the best algorithm is best-mi-transactions iterative multi-choice with 93.9% in an average running time of 0.003 s. [ABSTRACT FROM AUTHOR]

In this paper, the single-machine scheduling problems under the common and slack due date assignments are studied, where the actual processing time of the job needs to consider some factors, such as convex resource allocation, maintenance activity, and learning effects. The goal of this study is to find the optimal sequence, maintenance activity location, resource allocation and common due date (flow allowance). The objective function is (1) to minimize the sum of scheduling cost (including the weighted sum of earliness, tardiness and common due date (flow allowance), where the weights are position-dependent weights) and resource consumption cost, and (2) to minimize the scheduling cost under the resource consumption cost which is bounded. We prove that these problems can be solved in polynomial time. [ABSTRACT FROM AUTHOR]

Employing the cognitive radio (CR) technology in IoT networks, referred to as CR-IoT, is considered a promising solution for providing the spectrum opportunities needed for massive IoT deployments. Jamming attacks can significantly increase energy consumption in CR-IoT networks by increasing the number of dropped packets, and hence the number of needed packet re-transmissions. Designing jamming-aware communication protocols that attempt to reduce the number of dropped packets in the network results in green CR-IoT networking. In this paper, we develop an energy-efficient, QoS-constrained, and jamming-aware routing scheme for green CR-IoT networks. The proposed routing protocol employs a probabilistic channel assignment scheme that provides reliable data delivery under both dynamic and static jamming attacks. The underlying channel assignment problem is mathematically formulated as a binary linear programming optimization problem with the goal of maximizing the end-to-end throughput using the least number of frequency channels while meeting a set of QoS requirements. This optimization is known to be NP-hard. The sequential fixing technique is adopted to provide a sub-optimal solution in polynomial time. Simulation results indicate that the proposed routing scheme provides a remarkable performance improvement over existing schemes. [ABSTRACT FROM AUTHOR]

Under just-in-time production, this paper studies a single machine common due-window (denoted by CONW) assignment scheduling problem with position-dependent weights and resource allocations. A job's actual processing time can be determined by the resource assigned to the job. A resource allocation model is divided into linear and convex resource allocations. Under the linear and convex resource allocation models, our goal is to find an optimal due-window location, job sequence and resource allocation. We prove that the weighted sum of scheduling cost (including general earliness–tardiness penalties with positional-dependent weights) and resource consumption cost minimization is polynomially solvable. In addition, under the convex resource allocation, we show that scheduling (resp. resource consumption) cost minimization is solvable in polynomial time subject to the resource consumption (resp. scheduling) cost being bounded. [ABSTRACT FROM AUTHOR]

This paper considers the single machine scheduling problem with due window, delivery time and deteriorating job, whose goal is to minimize the window location, window size, earliness and tardiness. Common due window and slack due window are considered. The delivery time depends on the actual processing time of past sequences. The actual processing time of the job is an increasing function of the start time. Based on the small perturbations technique and adjacent exchange technique, we obtain the propositions of the problems. For common and slack due window assignment, we prove that the two objective functions are polynomial time solvable in O (n l o g n) time. We propose the corresponding algorithms to obtain the optimal sequence, window location and window size. [ABSTRACT FROM AUTHOR]

This paper integrates, from a tactical perspective, berth allocation and quay-crane assignment, two important, closely related decisions in container terminal operations in a single model. To obtain optimal solutions, a branch-and-price algorithm is sought in this paper under the framework of Dantzig–Wolfe decomposition. The algorithm decomposes the original problem to a master problem that links all vessels competing for the shared resources of berths and quay cranes and multiple per-vessel pricing subproblems that can be solved efficiently in polynomial time. Specifically, in the stage of generating promising initial feasible columns, three heuristics are adopted; during the column-updating stage, the subgradient-based Lagrangian relaxation is introduced to tackle the possibly encountered degeneracy phenomenon; the branching strategy is implemented in the pricing subproblem rather than in the master problem as reported in the literature with the benefit of avoiding incurring new dual prices, simplifying the branching process; and both breadth- and depth-first searching policies are tested to select the next node to explore. With real-life data, extensive numerical experiments are conducted to select the best choice for each stage with the strengths and drawbacks of each choice provided. And then the superiority of the branch-and-price algorithm configured with the selected combination of strategies is verified by comparing it with both CPLEX, a general-purpose solver, and a set-partitioning model, a dedicated algorithm reported in the literature. In addition, the decomposition by vessels adopted in this paper is also verified numerically by comparing it with the decomposition by berths reported in the literature, and the performance of the algorithm for other problem settings has also been tested. In conclusion, the numerical experiments show that our method outperforms the commercial solver and state-of-the-art solution methods reported in the literature in terms of both solution quality and computational time. [ABSTRACT FROM AUTHOR]

The Exact Satisfiability problem asks if we can find a satisfying assignment to each clause such that exactly one literal in each clause is assigned 1, while the rest are all assigned 0. We can generalise this problem further by defining that a C j clause is solved iff exactly j of the literals in the clause are 1 and all others are 0. We now introduce the family of Generalised Exact Satisfiability problems called G i XSAT as the problem to check whether a given instance consisting of C j clauses with j ∈ { 0 , 1 , ... , i } for each clause has a satisfying assignment. In this paper, we present faster exact polynomial space algorithms, using a nonstandard measure, to solve G i XSAT, for i ∈ { 2 , 3 , 4 } , in O (1.3674 n) time, O (1.5687 n) time and O (1.6545 n) time, respectively, using polynomial space, where n is the number of variables. This improves the current state of the art for polynomial space algorithms from O (1.4203 n) time for G2XSAT by Zhou, Jiang and Yin and from O (1.6202 n) time for G3XSAT by Dahllöf and from O (1.6844 n) time for G4XSAT which was by Dahllöf as well. In addition, we present faster exact algorithms solving G2XSAT, G3XSAT and G4XSAT in O (1.3188 n) time, O (1.3407 n) time and O (1.3536 n) time respectively at the expense of using exponential space. [ABSTRACT FROM AUTHOR]

We revisit the maximum satisfiability problem (Max-SAT) in the data stream model. In this problem, the stream consists of m clauses that are disjunctions of literals drawn from n Boolean variables. The objective is to find an assignment to the variables that maximizes the number of satisfied clauses. Chou et al. (FOCS 2020) showed that Ω (n) space is necessary to yield a 2 / 2 + ε approximation of the optimum value; they also presented an algorithm that yields a 2 / 2 − ε approximation of the optimum value using O (ε − 2 log ⁡ n) space. In this paper, we not only focus on approximating the optimum value, but also on obtaining the corresponding Boolean assignment using sublinear o (m n) space. We present randomized single-pass algorithms that w.h.p.1 yield: • A 1 − ε approximation using O ˜ (n / ε 3) space and exponential post-processing time • A 3 / 4 − ε approximation using O ˜ (n / ε) space and polynomial post-processing time. Our ideas also extend to dynamic streams. However, we show that the streaming k -SAT problem, which asks whether one can satisfy all size- k input clauses, must use Ω (n k) space. We also consider the related minimum satisfiability problem (Min-SAT), introduced by Kohli et al. (SIAM J. Discrete Math. 1994), that asks to find an assignment that minimizes the number of satisfied clauses. For this problem, we give a O ˜ (n 2 / ε 2) space algorithm, which is sublinear when m = ω (n) , that yields an α + ε approximation where α is the approximation guarantee of the offline algorithm. If each variable appears in at most f clauses, we show that a 2 f n approximation using O ˜ (n) space is possible. Finally, for the Max-AND-SAT problem where clauses are conjunctions of literals, we show that any single-pass algorithm that approximates the optimal value up to a factor better than 1/2 with success probability at least 2/3 must use Ω (m n) space. [ABSTRACT FROM AUTHOR]

This paper studies single-machine due-window assignment scheduling problems with truncated learning effect and resource allocation simultaneously. Linear and convex resource allocation functions under common due-window (CONW) assignment are considered. The goal is to find the optimal due-window starting (finishing) time, resource allocations and job sequence that minimize a weighted sum function of earliness and tardiness, due window starting time, due window size, and total resource consumption cost, where the weight is position-dependent weight. Optimality properties and polynomial time algorithms are proposed to solve these problems. [ABSTRACT FROM AUTHOR]

We study the problem of assigning non-overlapping geometric objects centered at a given set of points such that the sum of area covered by them is maximized. The problem remains open since 2002, as mentioned in a lecture slide of David Eppstein. In this paper, we have performed an exhaustive study on the problem. We show that, if the points are placed in R 2 then the problem is NP-hard even for simplest type of covering objects like disks or squares. In contrast, Eppstein (2017) [10] proposed a polynomial time algorithm for maximizing the sum of radii (or perimeter) of non-overlapping disks when the points are arbitrarily placed in R 2. We show that Eppstein's algorithm for maximizing sum of perimeter of the disks in R 2 gives a 2-approximation solution for the sum of area maximization problem. We also propose a PTAS for the same problem. Our results can be extended in higher dimensions as well as for a class of centrally symmetric convex objects. [ABSTRACT FROM AUTHOR]

We consider a variant of the assignment problem where entries of the matrix belong to an ordinal scale L. The objective is to find the set of optimal assignments according to a particular dominance criterion which is relevant in the context of ordinal data. This paper aims is to explore the frontier between easy and hard cases depending on |L|, the size of the ordinal scale. We give a polynomial time algorithm that solve the problem for |L| = 3. When |L| is polynomial in the size of the instance we show that the decision version of the problem is NP-complete. [ABSTRACT FROM AUTHOR]

This paper studies joint device-to-device (D2D) group association and channel assignment in uplink multi-cell non-orthogonal multiple-access (NOMA) networks. Particularly, the goal is to assign D2D groups to cellular user channels at each base-station, while accounting for negative network externality due to the interference caused by pairing a user with a D2D group. To that end, a multi-objective signal-to-interference-plus-noise ratio (SINR)-maximizing power allocation solution procedure is proposed to determine the optimal power allocation for each (D2D group, user) pair, while meeting quality-of-service (QoS) requirements. After that, the joint D2D group association and channel assignment problem is modeled as a student-project allocation with preferences over (student, project) pairs matching problem. More specifically, two polynomial-time complexity stable matching algorithms are proposed to pair D2D groups with users, and associate them with base-stations. Simulation results are presented to evaluate the proposed matching algorithms when combined with the devised solution procedure, and compare them to a joint D2D group association, channel assignment and power allocation (J-GA-CA-PA) scheme. More importantly, the proposed algorithms are shown to efficiently yield comparable SINR—per user and D2D receiver—to the J-GA-CA-PA scheme, while maintaining QoS requirements. [ABSTRACT FROM AUTHOR]

In this paper we study the bilinear assignment problem (BAP) with size parameters m and n, $$m\le n$$ . BAP is a generalization of the well known quadratic assignment problem and the three dimensional assignment problem and hence NP-hard. We show that BAP cannot be approximated within a constant factor unless P = NP even if the associated quadratic cost matrix Q is diagonal. Further, we show that BAP remains NP-hard if $$m = O(\root r \of {n})$$ , for some fixed r, but is solvable in polynomial time if $$m = O\left( \frac{\log n}{\log \log n}\right) $$ . When the rank of Q is fixed, BAP is observed to admit FPTAS and when this rank is one, it is solvable in polynomial time under some additional restrictions. We then provide a necessary and sufficient condition for BAP to be equivalent to two linear assignment problems. A closed form expression to compute the average of the objective function values of all solutions is presented, whereas the median of the solution values cannot be identified in polynomial time, unless P = NP. We then provide polynomial time heuristic algorithms that find a solution with objective function value no worse than that of $$(m-1)!(n-1)!$$ solutions. However, computing a solution whose objective function value is no worse than that of $$m!n!-\lceil \frac{m}{\beta }\rceil !\lceil \frac{n}{\beta }\rceil !$$ solutions is NP-hard for any fixed rational number $$\beta >1$$ . [ABSTRACT FROM AUTHOR]

The paper focuses on cooperative games where the worth of any coalition of agents is determined by the optimal value of a matching problem on (possibly weighted) graphs. These games come in different forms that can be grouped in two broad classes, namely of matching and allocation games, and they have a wide spectrum of applications, ranging from two-sided markets where buyers and sellers are encoded as vertices in a graph, to allocation problems where indivisible goods have to be assigned (matched) to agents in a fair way, possibly using monetary compensations. The Shapley value and the related notion of Banzhaf value have often been identified as appropriate solution concepts for many applications of matching/allocation games, but their computation is intractable in general. It is known that these concepts can be computed in polynomial time for matching games on unweighted trees and on graphs having degree at most two. However, it was open whether or not such positive results could be extended to the more general case of graphs having bounded treewidth, and to the case of allocation problems on weighted graphs. The paper provides a positive answer to these questions, by showing that computing the Shapley value and the Banzhaf value is feasible in polynomial time for the following classes of games: matching games over unweighted graphs having bounded treewidth, allocation games over weighted graphs having bounded treewidth, and allocation games over weighted graphs and such that each good is of interest for two agents at most. Without such structural restrictions, computing these solution concepts on allocation games is instead shown to be #P-hard, even in the case of unweighted graphs. [ABSTRACT FROM AUTHOR]

This paper considers a single-machine scheduling problem with past-sequence-dependent delivery times and the truncated sum-of-processing-times-based learning effect. The goal is to minimize the total costs that comprise the number of early jobs, the number of tardy jobs and due date. The due date is a decision variable. There will be corresponding penalties for jobs that are not completed on time. Under the common due date, slack due date and different due date, we prove that these problems are polynomial time solvable. Three polynomial time algorithms are proposed to obtain the optimal sequence. [ABSTRACT FROM AUTHOR]