Towards Ambitious Approximation Algorithms in Stubborn Set Optimization

Reference:

Kimmo Varpaaniemi. Towards ambitious approximation algorithms in stubborn set optimization. In Hans-Dieter 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. Informatik-Bericht Nr. 161, Institut für Informatik, Humboldt-Universität zu Berlin, Germany, 2002.

Abstract:

This paper continues research on the stubborn set method that constructs on-the-fly a reduced LTS that is CFFD-equivalent 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/or-graph approach requires solving #P-complete counting problems in order to get the weights for the vertices of the and/or-graph. The ``branch-and-bound'' decision problem corresponding to the minimization of the sum of the computed weights is ``only'' NP-complete. Unfortunately, #P-complete counting does not seem easily avoidable in the general case because it is PP-complete 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/or-graphs, approximability in optimization and counting

Suggested BibTeX entry:

@inproceedings{VarpaaniemiKimmo-Vrp02c,
    author = {Kimmo Varpaaniemi},
    booktitle = {{W}orkshop: {C}oncurrency, Specification and Programming, {C}{S}\&{P}'2002, {B}erlin, {O}ctober 7--9, 2002, Volume 2},
    editor = {Hans-Dieter Burkhard and Ludwik Czaja and Gabriela Lindemann and Andrzej Skowron and Peter H. Starke},
    pages = {370--379},
    publisher = {Informatik-Bericht Nr. 161, Institut f{\"{u}}r Informatik, Humboldt-Universit{\"{a}}t zu Berlin, Germany},
    title = {{T}owards Ambitious Approximation Algorithms in Stubborn Set Optimization},
    year = {2002},
}