A New Approach to Cactus Construction Applied to TSP Support Graphs

Authors:
Klaus M. Wenger
Affiliations:
-
Venue:
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Year:
2002

Citing 12
Cited 2

Facet identification for the symmetric traveling salesman polytope

Mathematical Programming: Series A and B
The crown inequalities for the symmetric traveling salesman polytope

Mathematics of Operations Research
A faster algorithm for finding the minimum cut in a directed graph

SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A new approach to the minimum cut problem

Journal of the ACM (JACM)
Experimental study of minimum cut algorithms

SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Building chain and cactus representations of all minimum cuts from Hao-Orlin in the same asymptotic run time

Journal of Algorithms
Separating a Superclass of Comb Inequalities in Planar Graphs

Mathematics of Operations Research
The vehicle routing problem

The vehicle routing problem
Separating Maximally Violated Comb Inequalities in Planar Graphs

Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Finding Cuts in the TSP (A preliminary report)

Finding Cuts in the TSP (A preliminary report)
Cut structures and randomized algorithms in edge-connectivity problems

Cut structures and randomized algorithms in edge-connectivity problems
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms

Journal of Computer and System Sciences

Privatized rural postman problems

Computers and Operations Research
Generating partitions of a graph into a fixed number of minimum weight cuts

Discrete Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a novel approach to the construction of the cactus representation of all minimum cuts of a graph. The representation is a supergraph that stores the set of all mincuts compactly and mirrors its structure. We focus on support graphs occurring in the branch-andcut approach to traveling salesman, vehicle routing and similar problems in a natural way. The ideas presented also apply to more general graphs. Unlike most previous construction approaches, we do not follow the Karzanov-Timofeev framework or a variation of it. Our deterministic algorithm is based on inclusion-minimal mincuts. We use Fleischer's approach [J. Algorithms, 33(1):51-72, 1999], one of the fastest to date, as benchmark. The new algorithm shows an average speed-up factor of 20 for TSP-related support graphs in practice. We report computational results. Compared to the benchmark, we reduce the space required during construction for n-vertex graphs with m edges from O(n2) to O(m).