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Power Efficient Range Assignment for Symmetric Connectivity in Static Ad Hoc Wireless Networks

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Abstract

In this paper we study the problem of assigning transmission ranges to the nodes of a static ad hoc wireless network so as to minimize the total power consumed under the constraint that enough power is provided to the nodes to ensure that the network is connected. We focus on the Min-Power Symmetric Connectivity problem, in which the bidirectional links established by the transmission ranges are required to form a connected graph.

Implicit in previous work on transmission range assignment under asymmetric connectivity requirements is the proof that Min-Power Symmetric Connectivity is NP-hard and that the MST algorithm has a performance ratio of 2. In this paper we make the following contributions: (1) we show that the related Min-Power Symmetric Unicast problem can be solved efficiently by a shortest-path computation in an appropriately constructed auxiliary graph; (2) we give an exact branch and cut algorithm based on a new integer linear program formulation solving instances with up to 35–40 nodes in 1 hour; (3) we establish the similarity between Min-Power Symmetric Connectivity and the classic Steiner Tree problem in graphs, and use this similarity to give a polynomial-time approximation scheme with performance ratio approaching 5/3 as well as a more practical approximation algorithm with approximation factor 11/6; and (4) we give the results of a comprehensive experimental study comparing new and previously proposed heuristics with the above exact and approximation algorithms.

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Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, D-66123, Saarbrücken, Germany

    E. Althaus

  2. Department of Computer Science, Illinois Institute of Technology, Chicago, IL, 60616

    G. Călinescu & N. Tchervenski

  3. Computer Science and Engineering Department, University of Connecticut, 371 Fairfield Rd., Unit 2155, Storrs, CT, 06269

    I. I. Măndoiu

  4. Department of Computer Science, Georgia State University, Atlanta, GA, 30303

    S. Prasad & A. Zelikovsky

Authors
  1. E. Althaus
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  2. G. Călinescu
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  3. I. I. Măndoiu
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  4. S. Prasad
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  5. N. Tchervenski
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  6. A. Zelikovsky
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Corresponding author

Correspondence to E. Althaus.

Additional information

Ernst Althaus received the M.S. degree in 1998 and the Ph.D. degree in 2001, both in Computer Science, from the Universität des Saarlandes. He worked as a postdoctoral researcher at the International Computer Science Institute in Berkeley and at the Max-Planck-Institut für Informatik in Saarbrücken. Ernst Althaus is now the head of an independent research group on “optimization in bioinformatics” at the Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Nancy. His research interests include combinatorial optimization, bioinformatics, and algorithms.

Gruia Călinescu is an Assistant Professor of Computer Science at the Illinois Institute of Technology. He has a Diploma from University of Bucharest and a PhD from Georgia Institute of Technology. His research interests are in the area of algorithms.

Ion I. Măndoiu received the M.S. degree from Bucharest University in 1992 and the Ph.D. degree from Georgia Institute of Technology in 2000, both in Computer Science. He is now an Assistant Professor with the Computer Science and Engineering Department at the University of Connecticut. His research focuses on the design and analysis of exact and approximation algorithms for NP-hard optimization problems, particularly in the areas of VLSI computer aided design, bioinformatics, and ad-hoc wireless notworks. He authored over 40 refereed scientific publications in these areas, including a best paper at the joint Asia-South Pacific Design Automation/VLSI Design Conferences.

Sushil K. Prasad received his B. Tech. in Computer Science and Engineering from Indian Institute of Technology, Kharagpur, in 1985, M.S. in Computer Science from Washington State University, Pullman, in 1986, and Ph.D. in Computer Science from University of Central Florida, Orlando, in 1990. Since 1990, he has been a Professor of Computer Science at Georgia State University (GSU), Atlanta. Currently, as P.I. of the Yamacraw/GEDC Distributed, Mobile and Embedded Systems research contracts, he is leading a GSU team of seven faculty and 20 Ph.D./M.S. students on developing System on Mobile Devices (SyD) middleware for collaborative computing over heterogeneous mobile devices and data sources. Prasad has carried out theoretical as well as experimental research in parallel and distributed computing, with over 55 publications, and made 3 utility patent applications and over a dozen provisional patent applications. His current research interests are Parallel Algorithms and Data Structures, Parallel Discrete Event Simulation, Web-based Distributed and Collaborative Computing, and Middlewares and Collaborative Applications for Handheld Devices.

Nickolay Tchervenski received his B.S. in Computer Engineering with highest honors from Illinois Institute of Technology in 2004. At IIT, Nickolay was advised by Prof. Calinescu. In Fall 2004, Nickolay joined the Database Research Group at University of Waterloo where he is doing his Masters Degree in Computer Science. World finalist at the 28th ACM International Collegiate Programming Contest in Prague, Nickolay’s research interests are in algorithms and large databases.

Alexander Zelikovsky received the Ph.D. degree in Computer Science from the Institute of Mathematics of the Belorussian Academy of Sciences in Minsk (Belarus) in 1989 and worked at the Institute of Mathematics in Kishinev (Moldova) (1989–1995). Between 1992 and 1995 he visited Bonn University and the Institut fur Informatik in Saarbrueken (Germany). Dr. Zelikovsky was a Research Scientist at University of Virginia (1995–1997) and a Postdoctoral Scholar at UCLA (1997–1998). He is an Associate Professor at Computer Science Department of Georgia State University which he joined in 1999. He is the author of more than 90 refereed publications. Dr. Zelikovsky’s research interests include VLSI physical layout design, ad-hoc wireless networks, discrete and approximation algorithms, combinatorial optimization, and computational biology.

Preliminary versions of the results in this paper have appeared in [1, 11].

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Althaus, E., Călinescu, G., Măndoiu, I.I. et al. Power Efficient Range Assignment for Symmetric Connectivity in Static Ad Hoc Wireless Networks. Wireless Netw 12, 287–299 (2006). https://doi.org/10.1007/s11276-005-5275-x

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