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We study gossip algorithms for the rumor spreading problem, which asks each node to deliver a rumor to all nodes in an unknown network. Gossip algorithms allow nodes only to call one neighbor per round and have recently attracted attention as message efficient, simple, and robust solutions to the rumor spreading problem. A long series of papers analyzed the performance of uniform random gossip in which nodes repeatedly call a random neighbor to exchange all rumors with. A main result of this investigation was that uniform gossip completes in O(log n/Φ) rounds where Φ is the conductance of the network. Nonuniform random gossip schemes were devised to allow efficient rumor spreading in networks with bottlenecks. In particular, [Censor-Hillel et al., STOC'12] gave an O(log³ n) algorithm to solve the 1-local broadcast problem in which each node wants to exchange rumors locally with its 1-neighborhood. By repeatedly applying this protocol, one can solve the global rumor spreading quickly for all networks with small diameter, independently of the conductance. All these algorithms are inherently randomized in their design and analysis. A parallel research direction has been to reduce and determine the amount of randomness needed for efficient rumor spreading. This has been done via lower bounds for restricted models and by designing gossip algorithms with a reduced need for randomness, for instance, by using pseudorandom generators with short random seeds. The general intuition and consensus of these results has been that randomization plays a important role in effectively spreading rumors and that at least a polylogarithmic number of random bit are crucially needed. In this article improves over the state of the art in several ways by presenting a deterministic gossip algorithm that solves the the k-local broadcast problem in 2(k + log2n) log2n rounds. Besides being the first efficient deterministic solution to the rumor spreading problem this algorithm is interesting in many aspects: It is simpler, more natural, more robust, and faster than its randomized pendant and guarantees success with certainty instead of with high probability. Its analysis is furthermore simple, self-contained, and fundamentally different from prior works. [ABSTRACT FROM AUTHOR]

After using evolutionary techniques for single-objective optimization during more than two decades, the incorporation of more than one objective in the fitness function has finally become a popular area of research. As a consequence, many new evolutionary-based approaches and variations of existing techniques have recently been published in the technical literature. The purpose of this paper is to summarize and organize the information on these current approaches, emphasizing the importance of analyzing the operations research techniques in which most of them are based, in an attempt to motivate researchers to look into these mathematical programming approaches for new ways of exploiting the search capabilities of evolutionary algorithms. Furthermore, a summary of the main algorithms behind these approaches is provided, together with a brief criticism that includes their advantages and disadvantages, degree of applicability, and some known applications. Finally, future trends in this area and some possible paths for further research are also addressed. [ABSTRACT FROM AUTHOR]

Systems in many safety-critical application domains are subject to certification requirements. For any given system, however, it may be the case that only a subset of its functionality is safety-critical and hence subject to certification; the rest of the functionality is non-safety-critical and does not need to be certified, or is certified to lower levels of assurance. The certification-cognizant runtime scheduling of such mixedcriticality systems is considered. An algorithm called EDF-VD (for Earliest Deadline First with Virtual Deadlines) is presented: this algorithm can schedule systems for which any number of criticality levels are defined. Efficient implementations of EDF-VD, as well as associated schedulability tests for determining whether a task system can be correctly scheduled using EDF-VD, are presented. For up to 13 criticality levels, analyses of EDF-VD, based on metrics such as processor speedup factor and utilization bounds, are derived, and conditions under which EDF-VD is optimal with respect to these metrics are identified. Finally, two extensions of EDF-VD are discussed that enhance its applicability. The extensions are aimed at scheduling a wider range of task sets, while preserving the favorable worst-case resource usage guarantees of the basic algorithm. [ABSTRACT FROM AUTHOR]

Because of the natural way in which subsystems are cast into subproblems, resource- directive decomposition methods of mathematical programming problems have attracted considerable attention in recent years. A review of the specialized literature is presented in this paper, where the features and drawbacks of the most representative resource-directive methods are analyzed. To give an appropriate chronological and technical perspective, early general methods, such as the ones of Dantzig-Wolfe and Benders, are also included in the survey. [ABSTRACT FROM AUTHOR]

Let f be a function on a set of variables V. For each x ∈ V, let c(x) be the cost of reading the value of x. An algorithm for evaluating f is a strategy for adaptively identifying and reading a set of variables U ⊆ V whose values uniquely determine the value of f . We are interested in finding algorithms which minimize the cost incurred to evaluate f in the above sense. Competitive analysis is employed to measure the performance of the algorithms. We address two variants of the above problem. We consider the basic model in which the evaluation algorithm knows the cost c(x), for each x ∈ V. We also study a novel model where the costs of the variables are not known in advance and some preemption is allowed in the reading operations. This model has applications, for example, when reading a variable coincides with obtaining the output of a job on a CPU and the cost is the CPU time. For the model where the costs of the variables are known, we present a polynomial time algorithm with the best possible competitive ratio γ f c for each function f that is representable by a threshold tree and for each fixed cost function c(·). Remarkably, the best-known result for the same class of functions is a pseudo-polynomial algorithm with competitiveness 2γ f c . Still in the same model, we introduce the Linear Programming Approach (LPA), a framework that allows the design of efficient algorithms for evaluating functions. We show that different implementations of this approach lead in general to the best algorithms known so far—and in many cases to optimal algorithms—for different classes of functions considered before in the literature. Via the LPA, we are able to determine exactly the optimal extremal competitiveness of monotone Boolean functions. Remarkably, the upper bound which leads to this result, holds for a much broader class of functions, which also includes the whole set of Boolean functions. We also show how to extend the LPA (together with these results) to the model where the costs of the variables are not known beforehand. In particular, we show how to employ the extended LPA to design a polynomial-time optimal (with respect to competitiveness) algorithm for the class of monotone Boolean functions representable by threshold trees. [ABSTRACT FROM AUTHOR]

The Johnson-Lindenstrauss lemma shows that any n points in Euclidean space (i.e., ℝn with distances measured under the ℓ2 norm) may be mapped down to O((log n)/ε²) dimensions such that no pairwise distance is distorted by more than a (1 + ε) factor. Determining whether such dimension reduction is possible in ℓ1 has been an intriguing open question. We show strong lower bounds for general dimension reduction in ℓ1. We give an explicit family of n points in ℓ1 such that any embedding with constant distortion D requires nΩ(1/D²) dimensions. This proves that there is no analog of the Johnson-Lindenstrauss lemma for ℓ1; in fact, embedding with any constant distortion requires nΩ(1) dimensions. Further, embedding the points into ℓ1 with (1 + ε) distortion requires n½-O(ε(1/ε)) dimensions. Our proof establishes this lower bound for shortest path metrics of series-parallel graphs. We make extensive use of linear programming and duality in devising our bounds. We expect that the tools and techniques we develop will be useful for future investigations of embeddings into ℓ1. [ABSTRACT FROM AUTHOR]

Consider an n-vertex graph G = (V, E) of maximum degree ?, and suppose that each vertex v ? V hosts a processor. The processors are allowed to communicate only with their neighbors in G. The communication is synchronous, that is, it proceeds in discrete rounds. [ABSTRACT FROM AUTHOR]