TY - GEN

T1 - Discounted deterministic Markov decision processes and discounted all-pairs shortest paths

AU - Madani, Omid

AU - Thorup, Mikkel

AU - Zwick, Uri

PY - 2009

Y1 - 2009

N2 - We present two new algorithms for finding optimal strategies for discounted, infinite-horizon, Deterministic Markov Decision Processes (DMDP). The first one is an adaptation of an algorithm of Young, Tarjan and Orlin for finding minimum mean weight cycles. It runs in O(mn + n2 log n) time, where n is the number of vertices (or states) and m is the number of edges (or actions). The second one is an adaptation of a classical algorithm of Karp for finding minimum mean weight cycles. It runs in O(mn) time. The first algorithm has a slightly slower worst-case complexity, but is faster than the first algorithm in many situations. Both algorithms improve on a recent O(mn 2)-time algorithm of Andersson and Vorobyov. We also present a randomized Õ(m1/2n2)-time algorithm for finding Discounted All-Pairs Shortest Paths (DAPSP), improving several previous algorithms.

AB - We present two new algorithms for finding optimal strategies for discounted, infinite-horizon, Deterministic Markov Decision Processes (DMDP). The first one is an adaptation of an algorithm of Young, Tarjan and Orlin for finding minimum mean weight cycles. It runs in O(mn + n2 log n) time, where n is the number of vertices (or states) and m is the number of edges (or actions). The second one is an adaptation of a classical algorithm of Karp for finding minimum mean weight cycles. It runs in O(mn) time. The first algorithm has a slightly slower worst-case complexity, but is faster than the first algorithm in many situations. Both algorithms improve on a recent O(mn 2)-time algorithm of Andersson and Vorobyov. We also present a randomized Õ(m1/2n2)-time algorithm for finding Discounted All-Pairs Shortest Paths (DAPSP), improving several previous algorithms.

UR - http://www.scopus.com/inward/record.url?scp=70349115580&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973068.104

DO - 10.1137/1.9781611973068.104

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AN - SCOPUS:70349115580

SN - 9780898716801

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 958

EP - 967

BT - Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms

PB - Association for Computing Machinery (ACM)

T2 - 20th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 4 January 2009 through 6 January 2009

ER -