TY - GEN
T1 - Optimal online contention resolution schemes via ex-ante prophet inequalities
AU - Lee, Euiwoong
AU - Singla, Sahil
N1 - Publisher Copyright:
© Euiwoong Lee and Sahil Singla.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - Online contention resolution schemes (OCRSs) were proposed by Feldman, Svensson, and Zenklusen [11] as a generic technique to round a fractional solution in the matroid polytope in an online fashion. It has found applications in several stochastic combinatorial problems where there is a commitment constraint: on seeing the value of a stochastic element, the algorithm has to immediately and irrevocably decide whether to select it while always maintaining an independent set in the matroid. Although OCRSs immediately lead to prophet inequalities, these prophet inequalities are not optimal. Can we instead use prophet inequalities to design optimal OCRSs? We design the first optimal 1/2-OCRS for matroids by reducing the problem to designing a matroid prophet inequality where we compare to the stronger benchmark of an ex-ante relaxation. We also introduce and design optimal (1-1/e)-random order CRSs for matroids, which are similar to OCRSs but the arrival order is chosen uniformly at random.
AB - Online contention resolution schemes (OCRSs) were proposed by Feldman, Svensson, and Zenklusen [11] as a generic technique to round a fractional solution in the matroid polytope in an online fashion. It has found applications in several stochastic combinatorial problems where there is a commitment constraint: on seeing the value of a stochastic element, the algorithm has to immediately and irrevocably decide whether to select it while always maintaining an independent set in the matroid. Although OCRSs immediately lead to prophet inequalities, these prophet inequalities are not optimal. Can we instead use prophet inequalities to design optimal OCRSs? We design the first optimal 1/2-OCRS for matroids by reducing the problem to designing a matroid prophet inequality where we compare to the stronger benchmark of an ex-ante relaxation. We also introduce and design optimal (1-1/e)-random order CRSs for matroids, which are similar to OCRSs but the arrival order is chosen uniformly at random.
KW - Contention resolution
KW - Matroids
KW - Prophets
KW - Stochastic optimization
UR - http://www.scopus.com/inward/record.url?scp=85052510213&partnerID=8YFLogxK
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U2 - 10.4230/LIPIcs.ESA.2018.57
DO - 10.4230/LIPIcs.ESA.2018.57
M3 - Conference contribution
AN - SCOPUS:85052510213
SN - 9783959770811
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 26th European Symposium on Algorithms, ESA 2018
A2 - Bast, Hannah
A2 - Herman, Grzegorz
A2 - Azar, Yossi
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 26th European Symposium on Algorithms, ESA 2018
Y2 - 20 August 2018 through 22 August 2018
ER -