TY - GEN
T1 - The Worst-Case Complexity of Symmetric Strategy Improvement
AU - van Dijk, T.
AU - Loho, G.
AU - Maat, M.T.
N1 - Conference code: 32
PY - 2024/2/7
Y1 - 2024/2/7
N2 - Symmetric strategy improvement is an algorithm introduced by Schewe et al. (ICALP 2015) that can be used to solve two-player games on directed graphs such as parity games and mean payoff games. In contrast to the usual well-known strategy improvement algorithm, it iterates over strategies of both players simultaneously. The symmetric version solves the known worst-case examples for strategy improvement quickly, however its worst-case complexity remained open. We present a class of worst-case examples for symmetric strategy improvement on which this symmetric version also takes exponentially many steps. Remarkably, our examples exhibit this behaviour for any choice of improvement rule, which is in contrast to classical strategy improvement where hard instances are usually hand-crafted for a specific improvement rule. We present a generalized version of symmetric strategy iteration depending less rigidly on the interplay of the strategies of both players. However, it turns out it has the same shortcomings.
AB - Symmetric strategy improvement is an algorithm introduced by Schewe et al. (ICALP 2015) that can be used to solve two-player games on directed graphs such as parity games and mean payoff games. In contrast to the usual well-known strategy improvement algorithm, it iterates over strategies of both players simultaneously. The symmetric version solves the known worst-case examples for strategy improvement quickly, however its worst-case complexity remained open. We present a class of worst-case examples for symmetric strategy improvement on which this symmetric version also takes exponentially many steps. Remarkably, our examples exhibit this behaviour for any choice of improvement rule, which is in contrast to classical strategy improvement where hard instances are usually hand-crafted for a specific improvement rule. We present a generalized version of symmetric strategy iteration depending less rigidly on the interplay of the strategies of both players. However, it turns out it has the same shortcomings.
UR - http://www.scopus.com/inward/record.url?scp=85185222158&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.CSL.2024.24
DO - 10.4230/LIPIcs.CSL.2024.24
M3 - Conference contribution
SN - 9783959773102
SP - 24.1-24.19
BT - 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)
A2 - Murano, Aniello
A2 - Silva, Alexandra
T2 - 32nd EACSL Annual Conference on Computer Science Logic, CSL 2024
Y2 - 19 February 2024 through 23 February 2024
ER -