Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs

@article{Kaplan2005ApproximationAF,
  title={Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs},
  author={Haim Kaplan and Moshe Lewenstein and Nira Shafrir and Maxim Sviridenko},
  journal={J. ACM},
  year={2005},
  volume={52},
  pages={602-626}
}
A directed multigraph is said to be d-regular if the indegree and outdegree of every vertex is exactly d. By Hall's theorem, one can represent such a multigraph as a combination of at most n2 cycle covers, each taken with an appropriate multiplicity. We prove that if the d-regular multigraph does not contain more than ⌊d/2⌋ copies of any 2-cycle then we can find a similar decomposition into n2 pairs of cycle covers where each 2-cycle occurs in at most one component of each pair. Our proof is… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 113 CITATIONS, ESTIMATED 97% COVERAGE

Integer Programming and Combinatorial Optimization

  • Lecture Notes in Computer Science
  • 2010
VIEW 12 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Approximation algorithms for maximum latency and partial cycle cover

  • Discrete Optimization
  • 2009
VIEW 4 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Improved Approximation Ratios for Traveling Salesperson Tours and Paths in Directed Graphs

  • APPROX-RANDOM
  • 2007
VIEW 15 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

On Approximating Asymmetric TSP and Related Problems

VIEW 7 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

On Approximability of Bounded Degree Instances of Selected Optimization Problems

VIEW 7 EXCERPTS
CITES METHODS, RESULTS & BACKGROUND
HIGHLY INFLUENCED

35 / 44-approximation for Asymmetric maxTSP with Triangle Inequality

VIEW 4 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Approximately Fair Cost Allocation in Metric Traveling Salesman Games

  • Theory of Computing Systems
  • 2007
VIEW 5 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Improved Approximation Algorithms for Metric Max TSP

VIEW 4 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

FILTER CITATIONS BY YEAR

2004
2019

CITATION STATISTICS

  • 19 Highly Influenced Citations