TY - JOUR

T1 - A FRAMEWORK FOR THE SECRETARY PROBLEM ON THE INTERSECTION OF MATROIDS

AU - Feldman, Moran

AU - Svensson, Ola

AU - Zenklusen, Rico

N1 - Publisher Copyright:
© 2022 Moran Feldman, Ola Svensson, and Rico Zenklusen.

PY - 2022

Y1 - 2022

N2 - The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where elements arrive one-by-one in random order, revealing a weight upon arrival. The decision whether to select an element has to be taken immediately after its arrival. The different applications that map to the secretary problem ask for different constraint families to be handled. The most prominent ones are matroid constraints, which both capture many relevant settings and admit strongly competitive secretary algorithms. However, dealing with more involved constraints proved to be much more difficult, and strong algorithms are known only for a few specific settings. In this paper, we present a general framework for dealing with the secretary problem over the intersection of several matroids. This framework allows us to combine and exploit the large set of matroid secretary algorithms known in the literature. As one consequence, we get constant-competitive secretary algorithms over the intersection of any constant number of matroids whose corresponding (single-)matroid secretary problems are currently known to have a constant-competitive algorithm. Moreover, we show that our results extend to submodular objectives.

AB - The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where elements arrive one-by-one in random order, revealing a weight upon arrival. The decision whether to select an element has to be taken immediately after its arrival. The different applications that map to the secretary problem ask for different constraint families to be handled. The most prominent ones are matroid constraints, which both capture many relevant settings and admit strongly competitive secretary algorithms. However, dealing with more involved constraints proved to be much more difficult, and strong algorithms are known only for a few specific settings. In this paper, we present a general framework for dealing with the secretary problem over the intersection of several matroids. This framework allows us to combine and exploit the large set of matroid secretary algorithms known in the literature. As one consequence, we get constant-competitive secretary algorithms over the intersection of any constant number of matroids whose corresponding (single-)matroid secretary problems are currently known to have a constant-competitive algorithm. Moreover, we show that our results extend to submodular objectives.

KW - matroid intersection

KW - matroid secretary problem

KW - online algorithms

UR - http://www.scopus.com/inward/record.url?scp=85135220090&partnerID=8YFLogxK

U2 - 10.1137/21M1411822

DO - 10.1137/21M1411822

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AN - SCOPUS:85135220090

SN - 0097-5397

VL - 51

SP - 766

EP - 819

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 3

M1 - 3

ER -