The resource allocation problem deals with distributing a number of indivisible, nonshareable resources among a set of agents so as to optimizing social welfare. Assuming all agents to have additive utility functions ...
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ISBN:
(纸本)9781450319935
The resource allocation problem deals with distributing a number of indivisible, nonshareable resources among a set of agents so as to optimizing social welfare. Assuming all agents to have additive utility functions and focusing on two particular measures of social welfare, envy-ratio and average-Nash product, we investigate the two resulting optimization problems. We give the first hardness of approximation result for a factor better than 3/2 for the problem of minimum envy-ratio, and we design an FPTAS for the case when the number of agents is fixed. For the special case when the number of agents and the number of resources are equal, we show that the problem is even solvable in polynomial time. Next, we propose the first approximation algorithm for maximizing the average-Nash product in the general case, and we prove that this problem admits a PTAS if all agents' utility functions are the same. Finally, we study the problem of how hard it is to design a truthful mechanism for these two optimization problems.
Various Solutions for Vertex Cover algorithms are available in the world which are from NP-Complete class. There are several real world applications of Vertex Cover algorithm like different networks as Terrorist commu...
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ISBN:
(纸本)9781538639016
Various Solutions for Vertex Cover algorithms are available in the world which are from NP-Complete class. There are several real world applications of Vertex Cover algorithm like different networks as Terrorist communication n/w, Wireless communication n/w, Airline communication n/w. We are representing the comparative analysis of various subsisting algorithms like approximation algorithm, List(s) algorithm, Greedy technique and Alom's algorithm for the Vertex Cover problem in this paper. From the analysis, we came to know that the Alom's algorithm is giving optimized result among all Vertex Cover algorithms of every graph having large number of nodes where the approximation algorithm gives the worst response of the execution for huge graphs.
The capacity region of multihop wireless network is involved in many capacity optimization problems. However, the membership of the capacity region is NP-complete in general, and hence the direct application of capaci...
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ISBN:
(纸本)9781424458363
The capacity region of multihop wireless network is involved in many capacity optimization problems. However, the membership of the capacity region is NP-complete in general, and hence the direct application of capacity region is quite limited. As a compromise, we often substitute the capacity region with a polynomial approximate capacity subregion. In this paper, we construct polynomial mu-approximate capacity subregions of multihop wireless network under either 802.11 interference model or protocol interference model in which all nodes have uniform communication radii normalized to one and uniform interference radii rho >= 1. The approximation factor mu decreases with rho in general and is smaller than the best-known ones in the literature. For example, mu velence 3 when rho >= 2.2907 under the 802.11 interference model or when rho >= 4.2462 under the protocol interference model. Our construction exploits a nature of the wireless interference called strip-wise transitivity of independence discovered in this paper and utilize the independence polytopes of cocomparability graphs in a spatial-divide-conquer manner. We also apply these polynomial mu-approximate capacity subregions to compute mu-approximate solutions for maximum (concurrent).
We consider a delivery problem on a network in which nodes have supplies or demands for certain products and arcs have lengths satisfying the triangle inequality. A vehicle of infinite capacity travels through the net...
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Tabu search is a novel technique for solving combinatorial optimization problems. The process in which the tabu search method seeks to transcend local optimality is based on an evaluation function which chooses the hi...
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