3 research outputs found
Improved guarantees for the a priori TSP
We revisit the a priori TSP (with independent activation) and prove stronger
approximation guarantees than were previously known. In the a priori TSP, we
are given a metric space and an activation probability for each
customer . We ask for a TSP tour for that minimizes the
expected length after cutting short by skipping the inactive customers. All
known approximation algorithms select a nonempty subset of the customers
and construct a master route solution, consisting of a TSP tour for and two
edges connecting every customer to a nearest customer in
. We address the following questions. If we randomly sample the subset ,
what should be the sampling probabilities? How much worse than the optimum can
the best master route solution be? The answers to these questions (we provide
almost matching lower and upper bounds) lead to improved approximation
guarantees: less than 3.1 with randomized sampling, and less than 5.9 with a
deterministic polynomial-time algorithm.Comment: 39 pages, 6 figures, extended abstract to appear in the proceedings
of ISAAC 202
Improving the approximation ratio for capacitated vehicle routing
We devise a new approximation algorithm for capacitated vehicle routing. Our algorithm yields a better approximation ratio for general capacitated vehicle routing as well as for the unit-demand case and the splittable variant. Our results hold in arbitrary metric spaces. This is the first improvement upon the classical tour partitioning algorithm by Haimovich and Rinnooy Kan (Math Oper Res 10:527-542, 1985) and Altinkemer and Gavish (Oper Res Lett 6:149-158, 1987).ISSN:0025-5610ISSN:1436-464