An Exact Algorithm for TSP in Degree-3 Graphs Via Circuit Procedure and Amortization on Connectivity Structure

The paper presents an O ∗ ( 1 . 2312 n ) -time and polynomial-space algorithm for the traveling salesman problem in an n -vertex graph with maximum degree 3. This improves all previous time bounds of polynomial-space algorithms for this problem. Our algorithm is a simple branch-and-search algorithm...

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Bibliographic Details
Published in:	Algorithmica Vol. 74; no. 2; pp. 713 - 741
Main Authors:	Xiao, Mingyu, Nagamochi, Hiroshi
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.02.2016
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Theory of Computation Measure and conquer Traveling salesman problem Exact exponential algorithm Connectivity Graph algorithm
ISSN:	0178-4617, 1432-0541
Online Access:	Get full text
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Summary:	The paper presents an O ∗ ( 1 . 2312 n ) -time and polynomial-space algorithm for the traveling salesman problem in an n -vertex graph with maximum degree 3. This improves all previous time bounds of polynomial-space algorithms for this problem. Our algorithm is a simple branch-and-search algorithm with only one branch rule designed on a cut-circuit structure of a graph induced by unprocessed edges. To improve a time bound by a simple analysis on measure and conquer, we introduce an amortization scheme over the cut-circuit structure by defining the measure of an instance to be the sum of not only weights of vertices but also weights of connected components of the induced graph.
ISSN:	0178-4617 1432-0541
DOI:	10.1007/s00453-015-9970-4