We present approximation algorithms for two problems: Stochastic Boolean Function Evaluation (SBFE) and Stochastic Submodular Set Cover (SSSC). Our results for SBFE problems are obtained by reducing them to SSSC probl...
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During evolution, global mutations may modify the gene order in a genome. Such mutations are commonly referred to as rearrangement events. One of the most frequent rearrangement events observed in genomes are reversal...
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This work presents a comprehensive survey of the development of pseudogradient stochastic approximation algorithms with randomized input disturbance, considers the problems of their applicability in optimization probl...
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This work presents a comprehensive survey of the development of pseudogradient stochastic approximation algorithms with randomized input disturbance, considers the problems of their applicability in optimization problems with linear constraints, and discusses new possibilities to use them for multiagent control for load balancing of nodes in computational networks. Justifications of the algorithms' correctness and their optimal convergence rate are based on the foundational works of B.T. Polyak.
Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynom...
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ISBN:
(纸本)9783319130750;9783319130743
Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation algorithms. Our method features the use of approximation-preserving reductions, akin to the notion of parameterized reductions. We exemplify this method to obtain the currently best approximation algorithms for Harmless Set, Differential and Multiple Nonblocker, all of them can be considered in the context of securing networks or information propagation.
For addressing the One-Dimensional Road side unit Deployment (D1RD) problem, a greedy approximate algorithm named Greedy2P3E was proposed two years ago, and its approximation ratio was proved to be at least 2/3 for th...
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For addressing the One-Dimensional Road side unit Deployment (D1RD) problem, a greedy approximate algorithm named Greedy2P3E was proposed two years ago, and its approximation ratio was proved to be at least 2/3 for the D1RD problem with EQual-radius RSUs (D1RD-EQ problem). Can better or even tight approximations for Greedy2P3E be found? In this paper, approximation ratio of Greedy2P3E is re-inspected and tight approximation ratio is found. To this end, a greedy algorithm named Greedy3P4 is first proposed and proved to have a tight approximation ratio of 3/4 for the D1RD-EQ problem. Then, by using Greedy3P4 as a bridge, 3/4 is also proved to be the tight approximation ratio of Greedy2P3E and it is tight for all n >= 2. Comparative evaluations are performed on real cases using a real vehicle trajectory dataset. The results show that these greedy algorithms usually return near optimal solutions with a profit more than 98% of the optimal solutions, and the greedy algorithms well outperform the other typical algorithms tested.
The Street sweeping problem (SSP) is a variation of the Windy postman problem (WPP) in which we must construct two tours traversing every edge, and each edge must be traversed once in each direction: one on the first ...
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This paper presents a generic framework for the design and comparison of polynomial-time approximation algorithms for MINIMUM STAR BICOLORING. This generic framework is parameterized by algorithms which produce sequen...
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This paper presents a generic framework for the design and comparison of polynomial-time approximation algorithms for MINIMUM STAR BICOLORING. This generic framework is parameterized by algorithms which produce sequences of distance-2 independent sets. As our main technical result we show that, when the parameterized algorithm produces sequences of distance-2 independent sets that remove at least edges during each step, the generic framework produces a polynomial-time approximation algorithm for MINIMUM STAR BICOLORING that is always at least of optimal. Under the generic framework, we model two algorithms for MINIMUM STAR BICOLORING from the literature: Complete Direct Cover (CDC) [Hossain and Steihaug, Computing a sparse Jacobian matrix by rows and columns, Optim. Methods Softw. 10 (1998), pp. 33-48] and ASBC [Juedes and Jones, Coloring Jacobians revisited: A new algorithm for star and acyclic bicoloring, Optim. Methods Softw. 27(1-3) (2012), pp. 295-309]. We apply our main result to show approximation upper bounds of and , respectively, for these two algorithms. Our approximation upper bound for CDC is the first known approximation analysis for this algorithm. In addition to modelling CDC and ASBC, we use the generic framework to build and analyze three new approximation algorithms for MINIMUM STAR BICOLORING: MAX-NEIGHBORHOOD, MAX-RATIO, and LOCAL-SEARCH-k.
We provide polynomial-time approximately optimal Bayesian mechanisms for makespan minimization on unrelated machines as well as for max-min fair allocations of indivisible goods, with approximation factors of 2 and mi...
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ISBN:
(纸本)9781510813311
We provide polynomial-time approximately optimal Bayesian mechanisms for makespan minimization on unrelated machines as well as for max-min fair allocations of indivisible goods, with approximation factors of 2 and min{m-k+1, O(k~(1/2))} respectively, matching the approximation ratios of best known polynomialtime algorithms (for max-min fairness, the latter claim is true for certain ratios of the number of goods m to people k). Our mechanisms are obtained by establishing a polynomial-time approximation-sensitive reduction from the problem of designing approximately optimal mechanisms for some arbitrary objective O to that of designing bi-criterion approximation algorithms for the same objective O plus a linear allocation cost term. Our reduction is itself enabled by extending the celebrated "equivalence of separation and optimization" [27, 32] to also accommodate bi-criterion approximations. Moreover, to apply the reduction to the specific problems of makespan and max-min fairness we develop polynomial-time bi-criterion approximation algorithms for makespan minimization with costs and max-min fairness with costs, adapting the algorithms of [45], [10] and [4] to the type of bi-criterion approximation that is required by the reduction.
A subset L subset of V of a graph G = (V, E) is called a liar's dominating set of G if (i) vertical bar N-G[u] boolean AND L vertical bar >= 2 for every vertex u is an element of V, and (ii) vertical bar N-G [u...
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A subset L subset of V of a graph G = (V, E) is called a liar's dominating set of G if (i) vertical bar N-G[u] boolean AND L vertical bar >= 2 for every vertex u is an element of V, and (ii) vertical bar N-G [u] boolean OR N-G[v]) boolean AND L vertical bar >= 3 for every pair of distinct vertices u, v is an element of V. The MIN LIAR Dom SET problem is to find a liar's dominating set of minimum cardinality of a given graph G and the DECIDE LIAR Dom SET problem is the decision version of the MIN LIAR Dom SET problem. The DECIDE LIAR DOM SET problem is known to be NP-complete for general graphs. In this paper, we first present approximation algorithms and hardness of approximation results of the MIN LIAR Dom SET problem in general graphs, bounded degree graphs, and p-claw free graphs. We then show that the DECIDE LIAR Dom SET problem is NP-complete for doubly chordal graphs and propose a linear time algorithm for computing a minimum liar's dominating set in block graphs. (C) 2015 Elsevier B.V. All rights reserved.
Many social networks and complex systems are found to be naturally divided into clusters of densely connected nodes, known as community structure (CS). Finding CS is one of fundamental yet challenging topics in networ...
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ISBN:
(纸本)9781467395052
Many social networks and complex systems are found to be naturally divided into clusters of densely connected nodes, known as community structure (CS). Finding CS is one of fundamental yet challenging topics in network science. One of the most popular classes of methods for this problem is to maximize Newman's modularity. However, there is a little understood on how well we can approximate the maximum modularity as well as the implications of finding community structure with provable guarantees. In this paper, we settle definitely the approximability of modularity clustering, proving that approximating the problem within any (multiplicative) positive factor is intractable, unless P = NP. Yet we propose the first additive approximation algorithm for modularity clustering with a constant factor. Moreover, we provide a rigorous proof that a CS with modularity arbitrary close to maximum modularity Q_(OPT) might bear no similarity to the optimal CS of maximum modularity. Thus even when CS with near-optimal modularity are found, other verification methods are needed to confirm the significance of the structure.
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