An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure
Abstract
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 the previous time bounds of O^*(1.251^n) by Iwama and Nakashima and O^*(1.260^n) by Eppstein. Our algorithm is a simple branch-and-search algorithm. The only branch rule is 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2012
- DOI:
- 10.48550/arXiv.1212.6831
- arXiv:
- arXiv:1212.6831
- Bibcode:
- 2012arXiv1212.6831X
- Keywords:
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- Computer Science - Data Structures and Algorithms
- E-Print:
- 24 pages and 4 figures