Reference:
Kimmo Varpaaniemi. Towards ambitious approximation algorithms in stubborn set optimization. In HansDieter Burkhard, Ludwik Czaja, Gabriela Lindemann, Andrzej Skowron, and Peter H. Starke, editors, Workshop: Concurrency, Specification and Programming, CS&P'2002, Berlin, October 7–9, 2002, Volume 2, pages 370–379. InformatikBericht Nr. 161, Institut für Informatik, HumboldtUniversität zu Berlin, Germany, 2002.
Abstract:
This paper continues research on the stubborn set method that constructs onthefly a reduced LTS that is CFFDequivalent to the parallel composition of given LTSs. In particular, minimization of the number of successor states of a given state is reconsidered. The earlier suggested and/orgraph approach requires solving #Pcomplete counting problems in order to get the weights for the vertices of the and/orgraph. The ``branchandbound'' decision problem corresponding to the minimization of the sum of the computed weights is ``only'' NPcomplete. Unfortunately, #Pcomplete counting does not seem easily avoidable in the general case because it is PPcomplete to check whether a given stubborn set produces at most as many successor states as another given stubborn set. Instead of solving each of the subproblems, one could think of computing approximate solutions in such a way that the total effect of the approximations is a useful approximation itself. General approximation algorithms for propositional logic problems essentially suffice for the purpose.
Keywords:
LTSs, stubborn sets, and/orgraphs, approximability in optimization and counting
Suggested BibTeX entry:
@inproceedings{Vrp02c,
author = {Kimmo Varpaaniemi},
booktitle = {{W}orkshop: {C}oncurrency, Specification and Programming, {C}{S}\&{P}'2002, {B}erlin, {O}ctober 79, 2002, Volume 2},
editor = {HansDieter Burkhard and Ludwik Czaja and Gabriela Lindemann and Andrzej Skowron and Peter H. Starke},
pages = {370379},
publisher = {InformatikBericht Nr. 161, Institut f{\"{u}}r Informatik, HumboldtUniversit{\"{a}}t zu Berlin, Germany},
title = {{T}owards Ambitious Approximation Algorithms in Stubborn Set Optimization},
year = {2002},
}
