47 research outputs found
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 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
LIPIcs, Volume 261, ICALP 2023, Complete Volum
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum