NDLI: Random Shortest Paths: Non-Euclidean Instances for Metric Optimization Problems

Content Provider	Springer Nature Link
Author	Bringmann, Karl Engels, Christian Manthey, Bodo Rao, B. V. Raghavendra
Copyright Year	2014
Abstract	Probabilistic analysis for metric optimization problems has mostly been conducted on random Euclidean instances, but little is known about metric instances drawn from distributions other than the Euclidean. This motivates our study of random metric instances for optimization problems obtained as follows: Every edge of a complete graph gets a weight drawn independently at random. The distance between two nodes is then the length of a shortest path (with respect to the weights drawn) that connects these nodes. We prove structural properties of the random shortest path metrics generated in this way. Our main structural contribution is the construction of a good clustering. Then we apply these findings to analyze the approximation ratios of heuristics for matching, the traveling salesman problem (TSP), and the $$k$$ -median problem, as well as the running-time of the 2-opt heuristic for the TSP. The bounds that we obtain are considerably better than the respective worst-case bounds. This suggests that random shortest path metrics are easy instances, similar to random Euclidean instances, albeit for completely different structural reasons.
Starting Page	42
Ending Page	62
Page Count	21
File Format	PDF
ISSN	01784617
Journal	Algorithmica
Volume Number	73
Issue Number	1
e-ISSN	14320541
Language	English
Publisher	Springer US
Publisher Date	2014-06-19
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Random shortest paths First passage percolation Approximation algorithms Random metrics Algorithm Analysis and Problem Complexity Theory of Computation Mathematics of Computing Algorithms Computer Systems Organization and Communication Networks Data Structures, Cryptology and Information Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications

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