Competitive algorithms and lower bounds for online randomized call control in cellular networks

  • Authors:

  • Ioannis Caragiannis;Christos Kaklamanis;Evi Papaioannou

  • Affiliations:

  • Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, 26500 Rio, Greece;Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, 26500 Rio, Greece;Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, 26500 Rio, Greece

  • Venue:
  • Networks
  • Year:
  • 2008

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Abstract

We address an important communication issue arising in wirelesscellular networks that utilize frequency division multiplexing(FDM) technology. In such networks, many users within the samegeographical region (cell) can communicate simultaneously withother users of the network using distinct frequencies. The spectrumof the available frequencies is limited; thus, efficient solutionsto the call control problem are essential. The objective of thecall control problem is, given a spectrum of available frequenciesand users that wish to communicate, to maximize the benefit, i.e.,the number of users that communicate without signal interference.We consider cellular networks of reuse distance k ≥ 2 andwe study the online version of the problem using competitiveanalysis. In cellular networks of reuse distance 2, the previouslybest known algorithm that beats the lower bound of 3 on thecompetitiveness of deterministic algorithms, works on networks withone frequency, achieves a competitive ratio against obliviousadversaries, which is between 2.469 and 2.651, and uses a number ofrandom bits at least proportional to the size of the network. Wesignificantly improve this result by presenting a series of simplerandomized algorithms that have competitive ratios significantlysmaller than 3, work on networks with arbitrarily many frequencies,and use only a constant number of random bits or a comparable weakrandom source. The best competitiveness upper bound we obtain is16-7 using only four random bits. In cellular networks of reusedistance k 2, we present simple randomized online callcontrol algorithms with competitive ratios, which significantlybeat the lower bounds on the competitiveness of deterministic onesand use only O(log k) random bits. Also, we show newlower bounds on the competitiveness of online call controlalgorithms in cellular networks of any reuse distance. Inparticular, we show that no online algorithm can achievecompetitive ratio better than 2, 25-12, and 2.5, in cellularnetworks with reuse distance k ε {2, 3, 4}, k= 5, and k ≥ 6, respectively. © 2008 WileyPeriodicals, Inc. NETWORKS, 2008