Cycle Cover with Short Cycles

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Cycle Cover with Short Cycles
Cycle covering is a well-studied problem in computer science. In this paper, we develop approximation algorithms for variants of cycle covering problems which bound the size and/or length of the covering cycles. In particular, we give a ´½ · ÐÒ¾µ-approximation for the lane covering problem [4, 5] in weighted graphs with metric lengths on the edges and an Ç´ÐÒ µ approximation for the bounded cycle cover problem [11] with cycle-size bound in uniform graphs. Our techniques are based on interpreting a greedy algorithm (proposed and empirically evaluated by Ergun et al. [4, 5]) as a dual-fitting algorithm. We then find the approximation factor by bounding the solution of a factor-revealing non-linear program. These are the first non-trivial approximation algorithms for these problems. We show that our analysis is tight for the greedy algorithm, and change the process of the dual-fitting algorithm to improve the factor for small cycle bounds. Finally, we prove that variants ...
Nicole Immorlica, Mohammad Mahdian, Vahab S. Mirro
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Authors Nicole Immorlica, Mohammad Mahdian, Vahab S. Mirrokni
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