Hardness of Approximation in PSPACE and Separation Results for Pebble Games
2015 (English)In: Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, Institute of Electrical and Electronics Engineers (IEEE), 2015, 466-485 p.Conference paper (Refereed)Text
We consider the pebble game on DAGs with bounded fan-in introduced in [Paterson and Hewitt '70] and the reversible version of this game in [Bennett '89], and study the question of how hard it is to decide exactly or approximately the number of pebbles needed for a given DAG in these games. We prove that the problem of deciding whether s pebbles suffice to reversibly pebble a DAG G is PSPACE-complete, as was previously shown for the standard pebble game in [Gilbert, Lengauer and Tarjan '80]. Via two different graph product constructions we then strengthen these results to establish that both standard and reversible pebbling space are PSPACE-hard to approximate to within any additive constant. To the best of our knowledge, these are the first hardness of approximation results for pebble games in an unrestricted setting (even for polynomial time). Also, since [Chan '13] proved that reversible pebbling is equivalent to the games in [Dymond and Tompa '85] and [Raz and McKenzie '99], our results apply to the Dymond - Tompa and Raz - McKenzie games as well, and from the same paper it follows that resolution depth is PSPACE-hard to determine up to any additive constant. We also obtain a multiplicative logarithmic separation between reversible and standard pebbling space. This improves on the additive logarithmic separation previously known and could plausibly be tight, although we are not able to prove this. We leave as an interesting open problem whether our additive hardness of approximation result could be strengthened to a multiplicative bound if the computational resources are decreased from polynomial space to the more common setting of polynomial time. © 2015 IEEE.
Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2015. 466-485 p.
Dymond-Tompa game, pebbling, PSPACE-complete, PSPACE-hardness of approximation, Raz-Mc Kenzie game, resolution depth, reversible pebbling, separation
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-186800DOI: 10.1109/FOCS.2015.36ISI: 000379204700027ScopusID: 2-s2.0-84960371365ISBN: 9781467381918OAI: oai:DiVA.org:kth-186800DiVA: diva2:928552
56th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2015, 17 October 2015 through 20 October 2015
QC 201605162016-05-162016-05-132016-08-12Bibliographically approved