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On the approximability of maximum and minimum edge clique partition problems

INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE 2007年第2期18卷 217-226页

作者： Dessmark, Anders Lingas, Andrzej Lundell, Eva-Marta Persson, Mia Jansson, Jesper Lund Univ Dept Comp Sci SE-22100 Lund Sweden Kyushu Univ Dept Comp Sci & Commun Engn Theoret Comp Sci Grp Yamashita LabNishi Ku Fukuoka 8190395 Japan

We consider the following clustering problems: given an undirected graph, partition its vertices into disjoint clusters such that each cluster forms a clique and the number of edges within the clusters is maximized (Max-ECP), or the number of edges between clusters is minimized (Min-ECP). These problems arise naturally in the DNA clone classification. We investigate the hardness of finding such partitions and provide approximation algorithms. Further, we show that greedy strategies yield constant factor approximations for graph classes for which maximum cliques can be found efficiently.

关键词： approximation algorithm clustering clique partition inapproximability DNA clone classification

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approximation algorithms for the bi-criteria weighted _MAX-CUT problem

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31st International Workshop on Graph-Theoretic Concepts in Computer Science

作者： Angel, Eric Bampis, Evripidis Gourves, Laurent Univ Evry Val Essonne LaMI CNRS UMR 8042 Evry France

ISBN: (纸本)3540310002

We consider a generalization of the classical MAX-CUT problem where two objective functions are simultaneously considered. We derive some theorems on the existence and the non-existence of feasible cuts that are at the same time near optimal for both criteria. Furthermore, two approximation algorithms with performance guarantee are presented. The first one is deterministic while the second one is randomized. A generalization of these results is given for the bi-criteria MAX-k-CUT problem. (c) 2006 Elsevier B.V. All rights reserved.

关键词： multicriteria optimization bicriteria (MAX-CUT) problem approximation algorithm performance guarantee

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Efficient algorithms for airline problem

Efficient algorithms for airline problem

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4th International Conference on Theory and Applications of Models of Computation

作者： Nakano, Shin-ichi Uehara, Ryuhei Uno, Takeaki Gunma Univ Fac Engn Dept Comp Sci Gunma 3768515 Japan Japan Adv Inst Sci &Technol Sch Informat Sci Ishikawa 9231292 Japan Natl Inst Informat Chiyoda-ku Tokyo 1018430 Japan

ISBN: (纸本)9783540725039

The airlines in the real world form small-world network. This implies that they are constructed with an ad hoc strategy. The small-world network is not so bad from the viewpoints of customers and managers. The customers can fly to any destination through a few airline hubs, and the number of airlines is not so many comparing to the number of airports. However, clearly, it is not the best solution in either viewpoint since there is a trade off. In this paper, one of the extreme cases, which is the standpoint of the manager, is considered;we assume that customers are silent and they never complain even if they are required to transit many times. This assumption is appropriate for some transportation service and packet communication. Under this assumption, the airline problem is to construct the least cost connected network for given distribution of the populations of cities with no a priori connection. First, we show an efficient algorithm that produces a good network which is minimized the number of vacant seats. The resultant network contains at most n connections (or edges), where n is the number of cities. Next we aim to minimize not only the number of vacant seats, but also the number of airline connections. The connected network with the least number of edges is a tree which has exactly n - 1 connections. However, the problem to construct a tree airline network with the minimum number of vacant seats is NP-complete. We also propose efficient approximation algorithms to construct a tree airline network with the minimum number of vacant seats.

关键词： airline problem approximation algorithm efficient algorithm NP-completeness

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Analytical performance evaluation of distributed multicast algorithms for directional communications in WANETs

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6th International IFIP-TC 6 Networking Conference

作者： Guo, Song Yang, Oliver Leung, Victor Univ Northern British Columbia Comp Sci Prince George BC V2L 5P2 Canada Univ Ottawa Sch Informat Technol & Engn Ottawa ON Canada Univ British Columbia Elect & Comp Engn Vancouver BC V5Z 1M9 Canada

ISBN: (纸本)97830540726050

Two distributed algorithms DMMT-OA and DMMT-DA have been recently proposed to maximize the multicast lifetime for directional communications in wireless ad-hoc networks. The experimental results have shown their superior performance than other centralized algorithms;however, their theoretical performance in terms of approximation ratio is still unknown. In this paper, we use graph theoretic approach to derive the approximation ratio for both algorithms. Furthermore, we have discovered by the first time that both ratios are bounded by a constant number.

关键词： wireless ad hoc networks approximation algorithm multicast distributed algorithm directional communications

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Sorting by weighted reversals, transpositions, and inverted transpositions

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10th Annual International Conference on Research in Computational Molecular Biology

作者： Bader, Martin Ohlebusch, Enno Univ Ulm Fac Engn & Comp Sci D-89069 Ulm Germany

ISBN: (纸本)3540332952

During evolution, genomes are subject to genome rearrangements that alter the ordering and orientation of genes on the chromosomes. If a genome consists of a single chromosome (like mitochondrial, chloroplast, or bacterial genomes), the biologically relevant genome rearrangements are (1) inversions-also called reversals-where a section of the genome is excised, reversed in orientation, and reinserted and (2) transpositions, where a section of the genome is excised and reinserted at a new position in the genome;if this also involves an inversion, one speaks of an inverted transposition. To reconstruct ancient events in the evolutionary history of organisms, one is interested in finding an optimal sequence of genome rearrangements that transforms a given genome into another genome. It is well known that this problem is equivalent to the problem of "sorting" a signed permutation into the identity permutation. In this paper, we provide a 1.5-approximation algorithm for sorting by weighted reversals, transpositions and inverted transpositions for biologically realistic weights.

关键词： approximation algorithm genome rearrangements weighted reversals and transpositions

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Degree-Constrained Network Flows 07

Degree-Constrained Network Flows

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39th Annual ACM Symposium on Theory of Computing

作者： Donovan, Patrick Shepherd, Bruce Vetta, Adrian Wilfong, Gordon McGill Univ Sch Comp Sci Montreal PQ H3A 2T5 Canada

ISBN: (纸本)9781595936318

A d-furcated flow is a network flow whose support graph has maximum outdegree d. Take a single-sink multicommodity How problem on any network and with any set of routing demands. Then we show that;the existence of feasible fractional flow with node congestion one implies the existence of a d-furcated How with congestion at most :1+1/d-1, for d >= 2. This result is tight, and so the congestion gap for d-furcated flows is bounded and exactly equal to 1 + 1/d-1, for the case d = 1. (confluent flows), it is known that the congestion gap is unbounded, namely circle minus(logn). Thus, allowing single-sink multicommodity network flows to increase their maximum outdegree from one to two virtually eliminates this previously observed congestion gap. As a corollary we obtain a factor 1 + 1/d-1-approximation algorithm for the problem of finding a minimum congestion d-furcated flow;we also prove that this problem is maxSNP-hard. Using known techniques these results also extend to degree-constrained unsplittable routing, where each individual demand must be routed along a unique path.

关键词： approximation algorithm multicommodity flows network flows confluent flows

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Clustered K-Center: Effective replica placement in Peer-to-Peer systems

Clustered K-Center: Effective replica placement in Peer-to-P...

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IEEE Global Telecommunications Conference (GLOBECOM 07)

作者： Zhou, Jian Zhang, Xin Bhuyan, Laxmi Liu, Bin Univ Calif Riverside Riverside CA 92521 USA Carnegie Mellon Univ Pittsburgh PA USA Tsinghua Univ Beijing Peoples R China

ISBN: (纸本)9781424410422

Peer-to-Peer (P2P) systems provide decentralization, self-organization, scalability and failure-resilience, but suffer from high worst-case latencies. Researchers have proposed various replication algorithms to place multiple copies of objects across the network in pursuit of better performance for P2P computing;nevertheless, they neither presented clear analysis nor derived worst-case bound for their algorithms. In this paper, we model the replica placement problem arising in real-world P2P networks as a Clustered K-Center problem which we prove to be NP-complete. Then we propose an efficient approximation algorithm to this problem with a provable upper bound. Extensive experiments have been conducted to demonstrate the effectiveness and efficiency of our algorithm. The experimental results show that our approach can run several orders of magnitude faster than the optimal solution while being able to minimizing the query latency.

关键词： replica placement Peer-to-Peer network Clustered K-Center problem approximation algorithm

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Server allocation algorithms for tiered systems

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11th Annual International Conference on Computing and Combinatorics (COCOON 2005)

作者： Chaudhuri, Kamalika Kothari, Anshul Pendavingh, Rudi Swaminathan, Ram Tarjan, Robert Zhou, Yunhong Univ Calif Berkeley Div Comp Sci Berkeley CA 94720 USA Univ Calif Santa Barbara Dept Comp Sci Santa Barbara CA 93106 USA TU Eindhoven Dept Math & Comp Sci Eindhoven Netherlands HP Labs Palo Alto CA 94304 USA Princeton Univ Dept Comp Sci Princeton NJ 08540 USA

ISBN: (纸本)9783540280613

Many web-based systems have a tiered application architecture, in which a request needs to transverse all the tiers before finishing its processing. One of the most important QoS metrics for these applications is the expected response time for the user. Since the expected response time in any tier depends upon the number of servers allocated to this tier, and a request's total response time is the sum of the response times over all the tiers, many different configurations (number of servers allocated to each tier) can satisfy the expected response-time requirement. Naturally, one would like to find the configuration that minimizes the total system cost while satisfying the total response-time requirement. This is modeled as a non-linear optimization problem using an open-queuing network model of response time, which we call the sen,er allocation problem for tiered systems (SAPTS). In this paper we study the computational complexity of SAPTS and design efficient algorithms to solve it. For a variable number of tiers, we show that the decision version of SAPTS is NP-complete. Then we design a simple two-approximation algorithm and a fully polynomial-time approximation scheme (FPTAS). If the number of tiers is a constant, we show that SAPTS is polynomial-time solvable. Furthermore, we design a fast polynomial-time exact algorithm to solve the important two-tier case. Most of our results extend to the general case in which each tier has an arbitrary response-time function.

关键词： combinatorial optimization approximation algorithm resource allocation multiple-choice knapsack problem tiered system

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On the approximability of maximum and minimum edge clique partition problems

On the approximability of maximum and minimum edge clique pa...

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12th Computing - The Australasian Theory Symposium (CATS 2006)

ISBN: (纸本)1920682333

关键词： approximation algorithm clustering clique partition inapproximability DNA clone classification

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A Min-Max optimization problem on traffic grooming in WDM optical networks

A Min-Max optimization problem on traffic grooming in WDM op...

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16th International Conference on Computer Communications and Networks

作者： Wang, Yong Gu, Qian-Ping Univ No British Columbia Dept Comp Sci Prince George BC V2N 4Z9 Canada Simon Fraser Univ Sch Comp Sci Burnaby BC V5A 1S6 Canada

ISBN: (纸本)9781424412501

In SONET/WDM networks, a wavelength channel is shared by multiplexed low-rate traffic demands. The multiplexing/de-multiplexing is known as traffic grooming and performed by SONET Add-Drop Multiplexers (SADM). The grooming factor, denoted by k, is the maximum number of low-rate traffic demands that can be multiplexed in one wavelength. Since SADMs are expensive, a key optimization problem in traffic grooming is to minimize the total number of required SADMs to satisfy the full connectivity for a given set of traffic demands. In this paper, we study traffic grooming from a different point of view. We consider a Min-Max optimization problem to minimize the number of SADMs at the network node where the number of required SADMs is the maximum over all nodes. We focus on the Unidirectional Path-Switched Ring networks with arbitrary duplex traffic demands. We prove the NP-hardness of this Min-Max optimization problem, and propose a linear time (k+1/2 + 2)-approximation algorithm. We then show that the approximation algorithm achieves the worst case lower bound. We also study the all-to-all traffic pattern, and propose an algorithm achieving solutions only a constant factor away from the optimal ones. Extensive simulations are conducted as well to validate the performance of our algorithm.

关键词： traffic grooming SONET/WDM networks graph partition NP-complete approximation algorithm

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