eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2010-12-14
436
446
10.4230/LIPIcs.FSTTCS.2010.436
article
Combinatorial Problems with Discounted Price Functions in Multi-agent Systems
Goel, Gagan
Tripathi, Pushkar
Wang, Lei
Motivated by economic thought, a recent research agenda has suggested the algorithmic study of combinatorial optimization problems under functions which satisfy the property of decreasing marginal cost. A natural first step to model such functions is to consider submodular functions. However, many fundamental problems have turned out to be extremely hard to approximate under general submodular functions, thus indicating the need for a systematic study of subclasses of submodular functions that are practically motivated and yield good approximation ratios. In this paper, we introduce and study an important subclass of submodular functions, which we call discounted price functions. These functions are succinctly representable and generalize linear(additive) price functions. We study the following fundamental combinatorial optimization problems: edge cover, spanning tree, perfect matching and $s-t$ path. We give both upper and lower bound for the approximability of these problems.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol008-fsttcs2010/LIPIcs.FSTTCS.2010.436/LIPIcs.FSTTCS.2010.436.pdf
Approximation algorithm
decreasing marginal cost
submodular function
discounted price function