Abstract
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 (1+ln 2)-approximation for the lane covering problem [3,4] in weighted graphs with metric lengths on the edges and an O(ln k) approximation for the bounded cycle cover problem [9] with cycle-size bound k in uniform graphs. Our techniques are based on interpreting a greedy algorithm (proposed and empirically evaluated by Ergun et al. [3,4]) 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 of the cycle cover problem which bound cycle size or length are APX-hard.
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Immorlica, N., Mahdian, M., Mirrokni, V.S. (2005). Cycle Cover with Short Cycles. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_53
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DOI: https://doi.org/10.1007/978-3-540-31856-9_53
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24998-6
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