Related papers: Secretary problem: graphs, matroids and greedoids
We study variants of the secretary problem, where $N$, the number of candidates, is a random variable, and the decision maker wants to maximize the probability of success -- picking the largest number among the $N$ candidates -- using only…
We study various generalizations of the secretary problem with submodular objective functions. Generally, a set of requests is revealed step-by-step to an algorithm in random order. For each request, one option has to be selected so as to…
We consider a dynamic model for competition in a social network, where two strategic agents have fixed beliefs and the non-strategic/regular agents adjust their states according to a distributed consensus protocol. We suppose that one…
The random-order or secretary model is one of the most popular beyond-worst case model for online algorithms. While it avoids the pessimism of the traditional adversarial model, in practice we cannot expect the input to be presented in…
We present a new variant of the secretary problem. Let $A$ be a totally ordered set of $n$ \emph{applicants}. Given $P\subseteq A$ and $x\in A$, let $rr(P,x)=\vert\{z\in P \mid z\leq x\}\vert\mbox{ }$ be the \emph{relative rank of} $x$…
We consider the online problem in which an intermediary trades identical items with a sequence of n buyers and n sellers, each of unit demand. We assume that the values of the traders are selected by an adversary and the sequence is…
This article studies two notions of generalized matroid representations motivated by algorithmic information theory and cryptographic secret sharing. The first (entropic representability) involves discrete random variables, while the second…
During the last decade, the matroid secretary problem (MSP) became one of the most prominent classes of online selection problems. Partially linked to its numerous applications in mechanism design, substantial interest arose also in the…
In the \textit{Matroid Secretary Problem} (MSP), the elements of the ground set of a Matroid are revealed on-line one by one, each together with its value. An algorithm for the MSP is \textit{Matroid-Unknown} if, at every stage of its…
Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, one must develop a decision mechanism that selects or dismisses the…
In the "secretary problem", well-known in the theory of optimal stopping, an employer is about to interview a maximum of N secretaries about which she has no prior information. Chow et al. proved that with an optimal strategy the expected…
The Sliding Window Secretary Problem allows a window of choices to the Classical Secretary Problem, in which there is the option to choose the previous $K$ choices immediately prior to the current choice. We consider a case of this…
This article is a survey of matroid theory aimed at algebraic geometers. Matroids are combinatorial abstractions of linear subspaces and hyperplane arrangements. Not all matroids come from linear subspaces; those that do are said to be…
We present various new results on greedoids. We prove a theorem that generalizes an equivalent formulation of Edmonds' classic matroid polytope theorem to local forest greedoids -- a class of greedoids that contains matroids as well as…
We study a variation of the game of best choice (also known as the secretary problem or game of googol) under an additional assumption that the ranks of interview candidates are restricted using permutation pattern-avoidance. We describe…
The problem of covering the ground set of two matroids by a minimum number of common independent sets is notoriously hard even in very restricted settings, i.e.\ when the goal is to decide if two common independent sets suffice or not.…
We investigate the parameterized complexity of finding diverse sets of solutions to three fundamental combinatorial problems, two from the theory of matroids and the third from graph theory. The input to the Weighted Diverse Bases problem…
We provide online algorithms for secretary matching in general weighted graphs, under the well-studied models of vertex and edge arrivals. In both models, edges are associated with arbitrary weights that are unknown from the outset, and are…
We define an independence system associated with simple graphs. We prove that the independence system is a matroid for certain families of graphs, including trees, with bases as minimal resolving sets. Consequently, the greedy algorithm on…
We characterize the shifted simple graphs and the $3$-uniform shifted hypergraphs whose inverse image under exterior shifting is the set of bases of a matroid: those are exactly the hypergraphs whose hyperedges form an initial lex-segment.…