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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Vydáno v:Algorithmica Ročník 74; číslo 2; s. 713 - 741
Hlavní autoři: Xiao, Mingyu, Nagamochi, Hiroshi
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.02.2016
Témata:
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
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Shrnutí: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