Structural Properties of Hard Metric TSP Inputs
2011 (English)In: SOFSEM 2011: THEORY AND PRACTICE OF COMPUTER SCIENCE / [ed] Cerna, I; Gyimothy, T; Hromkovic, J; Jeffery, K; Kralovic, R; Vukolic, M; Wolf, S, Springer Berlin/Heidelberg, 2011, 394-405 p.Conference paper (Refereed)
The metric traveling salesman problem is one of the most prominent APX-complete optimization problems. An important particularity of this problem is that there is a large gap between the known upper bound and lower bound on the approximability (assuming P not equal NP). In fact, despite more than 30 years of research, no one could find a better approximation algorithm than the 1.5-approximation provided by Christofides. The situation is similar for a related problem, the metric Hamiltonian path problem, where the start and the end of the path are prespecified: the best approximation ratio up to date is 5/3 by an algorithm presented by Hoogeveen almost 20 years ago. In this paper, we provide a tight analysis of the combined outcome of both algorithms. This analysis reveals that the sets of the hardest input instances of both problems are disjoint in the sense that any input is guaranteed to allow at least one of the two algorithms to achieve a significantly improved approximation ratio. In particular, we show that any input instance that leads to a 5/3-approximation with Hoogeveen's algorithm enables us to find an optimal solution for the traveling salesman problem. This way, we determine a set S of possible pairs of approximation ratios. Furthermore, for any input we can identify one pair of approximation ratios within S that forms an upper bound on the achieved approximation ratios.
Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2011. 394-405 p.
, Lecture Notes in Computer Science, ISSN 0302-9743 ; 6543
IdentifiersURN: urn:nbn:se:kth:diva-51298DOI: 10.1007/978-3-642-18381-2_33ISI: 000296264200033ScopusID: 2-s2.0-78751671636ISBN: 978-3-642-18380-5OAI: oai:DiVA.org:kth-51298DiVA: diva2:463857
37th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2011 JAN 22-28, 2011 Novy Smokovec, SLOVAKIA
QC 201112122011-12-122011-12-122012-01-15Bibliographically approved