4 research outputs found
On the best-choice prophet secretary problem
We study a variant of the secretary problem where candidates come from
independent, not necessarily identical distributions known to us, and show that
we can do at least as well as in the IID setting. This resolves a conjecture of
Esfandiari et al.Comment: 7 page
Towards an Optimal Contention Resolution Scheme for Matchings
In this paper, we study contention resolution schemes for matchings. Given a
fractional matching and a random set where each edge appears
independently with probability , we want to select a matching such that , for as large as
possible. We call such a selection method a -balanced contention resolution
scheme.
Our main results are (i) an asymptotically (in the limit as
goes to 0) optimal -balanced contention resolution scheme for
general matchings, and (ii) a -balanced contention resolution scheme for
bipartite matchings. To the best of our knowledge, this result establishes for
the first time, in any natural relaxation of a combinatorial optimization
problem, a separation between (i) offline and random order online contention
resolution schemes, and (ii) monotone and non-monotone contention resolution
schemes. We also present an application of our scheme to a combinatorial
allocation problem, and discuss some open questions related to van der
Waerden's conjecture for the permanent of doubly stochastic matrices.Comment: 22 page
A Tight Competitive Ratio for Online Submodular Welfare Maximization
In this paper we consider the online Submodular Welfare (SW) problem. In this problem we are given n bidders each equipped with a general non-negative (not necessarily monotone) submodular utility and m items that arrive online. The goal is to assign each item, once it arrives, to a bidder or discard it, while maximizing the sum of utilities. When an adversary determines the items\u27 arrival order we present a simple randomized algorithm that achieves a tight competitive ratio of 1/4. The algorithm is a specialization of an algorithm due to [Harshaw-Kazemi-Feldman-Karbasi MOR`22], who presented the previously best known competitive ratio of 3-2?2? 0.171573 to the problem. When the items\u27 arrival order is uniformly random, we present a competitive ratio of ? 0.27493, improving the previously known 1/4 guarantee. Our approach for the latter result is based on a better analysis of the (offline) Residual Random Greedy (RRG) algorithm of [Buchbinder-Feldman-Naor-Schwartz SODA`14], which we believe might be of independent interest
A Tight Competitive Ratio for Online Submodular Welfare Maximization
In this paper we consider the online Submodular Welfare (SW) problem. In this
problem we are given bidders each equipped with a general (not necessarily
monotone) submodular utility and items that arrive online. The goal is to
assign each item, once it arrives, to a bidder or discard it, while maximizing
the sum of utilities. When an adversary determines the items' arrival order we
present a simple randomized algorithm that achieves a tight competitive ratio
of \nicefrac{1}{4}. The algorithm is a specialization of an algorithm due to
[Harshaw-Kazemi-Feldman-Karbasi MOR`22], who presented the previously best
known competitive ratio of to the problem. When
the items' arrival order is uniformly random, we present a competitive ratio of
, improving the previously known \nicefrac{1}{4} guarantee.
Our approach for the latter result is based on a better analysis of the
(offline) Residual Random Greedy (RRG) algorithm of
[Buchbinder-Feldman-Naor-Schwartz SODA`14], which we believe might be of
independent interest