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Better Bounds for Incremental Frequency Allocation in Bipartite Graphs

  • Marek Chrobak
  • Łukasz Jeż
  • Jiří Sgall
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)

Abstract

We study frequency allocation in wireless networks. A wireless network is modeled by an undirected graph, with vertices corresponding to cells. In each vertex we have a certain number of requests, and each of those requests must be assigned a different frequency. Edges represent conflicts between cells, meaning that frequencies in adjacent vertices must be different as well. The objective is to minimize the total number of used frequencies.

The offline version of the problem is known to be NP-hard. In the incremental version, requests for frequencies arrive over time and the algorithm is required to assign a frequency to a request as soon as it arrives. Competitive incremental algorithms have been studied for several classes of graphs. For paths, the optimal (asymptotic) ratio is known to be 4/3, while for hexagonal-cell graphs it is between 1.5 and 1.9126. For ξ-colorable graphs, the ratio of (ξ + 1)/2 can be achieved.

In this paper, we prove nearly tight bounds on the asymptotic competitive ratio for bipartite graphs, showing that it is between 1.428 and 1.433. This improves the previous lower bound of 4/3 and upper bound of 1.5. Our proofs are based on reducing the incremental problem to a purely combinatorial (equivalent) problem of constructing set families with certain intersection properties.

Keywords

Wireless Network Bipartite Graph Chromatic Number Competitive Ratio Incremental Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Marek Chrobak
    • 1
  • Łukasz Jeż
    • 2
  • Jiří Sgall
    • 3
  1. 1.Department of Computer ScienceUniv. of CaliforniaRiversideUSA
  2. 2.Institute of Computer ScienceUniversity of WrocławWrocławPoland
  3. 3.Dept. of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPraha 1Czech Republic

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