Assign ranges in general ad-hoc networks

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Abstract

In this paper we theoretically study the MINIMUM RANGE ASSIGNMENT problem in static ad-hoc networks with arbitrary structure, where the transmission distances can violate triangle inequality. We consider two versions of the MINIMUM RANGE ASSIGNMENT problem, where the communication graph has to fulfill either the h-strong connectivity condition (MIN-RANGE(h-SC)) or the h-broadcast condition (MIN-RANGE(h-B)). Both homogeneous and non-homogeneous cases are studied. By approximating arbitrary edge-weighted graphs by paths, we present probabilistic O(logn)-approximation algorithms for MIN-RANGE(h-SC) and MIN-RANGE(h-B), which improves the previous best ratios O(lognloglogn) and O(n2lognloglogn), respectively [D. Ye, H. Zhang, The range assignment problem in static ad-hoc networks on metric spaces, Proceedings of the 11th Colloquium on Structural Information and Communication Complexity, Sirocco 2004, Lecture Notes in Computer Science, vol. 3104, pp. 291–302]. The result for MIN-RANGE(h-B) matches the lower bound [G. Rossi, The range assignment problem in static ad-hoc wireless networks. Ph.D. Thesis, 2003] for the case that triangle inequality for transmission distance holds (which is a special case of our model). Furthermore, we show that if the network fulfils certain property and the distance power gradient α is sufficiently small, the approximation ratio is improved to O((loglogn)α). Finally we discuss the applications of our algorithms in mobile ad-hoc networks.

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Janka Chlebíková received her M.Sc. degree in Mathematics from Charles University (Prague, Czechia) in 1988 and Ph.D. in Computer Science from Comenius University (Bratislava, Slovakia) in 2000. From 2001 to 2004 she had a postdoctoral fellowship at the Institute of Computer Science of CAU University in Kiel, Germany. She is working as an associate professor at the Institute of Informatics of Comenius University. Her research interests include structural graph theory, combinatorial optimization

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  • Cited by (3)

    Janka Chlebíková received her M.Sc. degree in Mathematics from Charles University (Prague, Czechia) in 1988 and Ph.D. in Computer Science from Comenius University (Bratislava, Slovakia) in 2000. From 2001 to 2004 she had a postdoctoral fellowship at the Institute of Computer Science of CAU University in Kiel, Germany. She is working as an associate professor at the Institute of Informatics of Comenius University. Her research interests include structural graph theory, combinatorial optimization and bioinformatics.

    Deshi Ye received his B.S. degree and Ph.D. degree in Mathematics from Zhejiang University, China, in 1999 and 2005, respectively. He is currently a research staff in the Department of Computer Science at the University of Hong Kong. His research interests include wireless network and mobile computing.

    Hu Zhang is currently a postdoc in the advanced optimization lab at McMaster University. He got his bachelor degree and a master degree in aerodynamics at Nanjing University of Aeronautics and Astronautics, and another master degree in mathematics at Hong Kong University of Science and Technology. He obtained his Ph.D. degree in theoretical computer science at University of Kiel, Germany. He is working on design, analysis and implementation of approximation algorithms for mathematical programming and combinatorial optimization problems, such as scheduling, VLSI design, digital communication.

    1

    This work was done in part when this author was working at the University of Kiel. Research supported in part by EU-Project ARACNE, Research Training Network, Approximation and Randomized Algorithms in Communication Networks, HPRN-CT-1999-00112.

    2

    This work was done in part when this author was studying at the University of Kiel. Research supported in part by a DAAD Sandwich Project and by NSFC(10231060).

    3

    This work was done in part when this author was studying at the University of Kiel. Research supported in part by the DFG Graduiertenkolleg 357, Effiziente Algorithmen und Mehrskalenmethoden by EU Thematic Network APPOL II, Approximation and Online Algorithms for Optimization Problems, IST-2001-32007, by EU Project CRESCCO, Critical Resource Sharing for Cooperation in Complex Systems, IST-2001-33135, by an MITACS grant of Canada, and by the NSERC Discovery Grant DG 5-48923.

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