Related papers: Matroid Secretary Problem in the Random Assignment…
In the paper the generalisation of the well known "secretary problem" is considered. The aim of the paper is to give a generalised model in such a way that the chosen set of the possible best $k$ elements have to be independent of all…
Contention resolution schemes have proven to be a useful and unifying abstraction for a variety of constrained optimization problems, in both offline and online arrival models. Much of prior work restricts attention to product distributions…
In classical secretary problems, a sequence of $n$ elements arrive in a uniformly random order, and we want to choose a single item, or a set of size $K$. The random order model allows us to escape from the strong lower bounds for the…
We examine several online matching problems, with applications to Internet advertising reservation systems. Consider an edge-weighted bipartite graph G, with partite sets L, R. We develop an 8-competitive algorithm for the following…
A matroid $\mathcal{M}$ on a set $E$ of elements has the $\alpha$-partition property, for some $\alpha>0$, if it is possible to (randomly) construct a partition matroid $\mathcal{P}$ on (a subset of) elements of $\mathcal{M}$ such that…
Only recently progress has been made in obtaining $o(\log(\mathrm{rank}))$-competitive algorithms for the matroid secretary problem. More precisely, Chakraborty and Lachish (2012) presented a $O(\sqrt{\log(\mathrm{rank})})$-competitive…
We study a twist on the classic secretary problem, which we term the secretary ranking problem: elements from an ordered set arrive in random order and instead of picking the maximum element, the algorithm is asked to assign a rank, or…
We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying…
For two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ defined on the same ground set $E$, the online matroid intersection problem is to design an algorithm that constructs a large common independent set in an online fashion. The algorithm is…
In the secretary problem we are faced with an online sequence of elements with values. Upon seeing an element we have to make an irrevocable take-it-or-leave-it decision. The goal is to maximize the probability of picking the element of…
Suppose that $n$ items arrive online in random order and the goal is to select $k$ of them such that the expected sum of the selected items is maximized. The decision for any item is irrevocable and must be made on arrival without knowing…
We study online secretary problems with returns in combinatorial packing domains with $n$ candidates that arrive sequentially over time in random order. The goal is to accept a feasible packing of candidates of maximum total value. In the…
Whereas there are simple algorithms that are proven to be optimal for the Classical and the Multiple Choice Secretary Problem, the Matroid Secretary Problem is less thoroughly understood. This paper proposes the generalization of some…
The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values…
Consider the following online version of the submodular maximization problem under a matroid constraint: We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent…
In the matroid buyback problem, an algorithm observes a sequence of bids and must decide whether to accept each bid at the moment it arrives, subject to a matroid constraint on the set of accepted bids. Decisions to reject bids are…
Random order online contention resolution schemes (ROCRS) are structured online rounding algorithms with numerous applications and links to other well-known online selection problems, like the matroid secretary conjecture. We are interested…
We study matroid prophet inequalities when distributions are unknown and accessible only through samples. While single-sample prophet inequalities for special matroids are known, no constant-factor competitive algorithm with even a…
We consider an online multi-weighted generalization of several classic online optimization problems, called the online combinatorial assignment problem. We are given an independence system over a ground set of elements and agents that…
The secretary problem is one of the fundamental problems in online decision making; a tight competitive ratio for this problem of $1/\mathrm{e} \approx 0.368$ has been known since the 1960s. Much more recently, the study of algorithms with…