47 research outputs found
An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure
Full text linkThe 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.Comment: 24 pages and 4 figure
LIPIcs, Volume 261, ICALP 2023, Complete Volume
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LIPIcs, Volume 248, ISAAC 2022, Complete Volume
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27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany
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