Related papers: The multi-returning secretary problem
In this paper, we discuss a stochastic decision problem of optimally selecting the order in which to try $n$ opportunities that may yield an uncertain reward in the future. The motivation came out from pure curiosity, after an informal…
We prove that for every proper minor-closed class $M$ of matroids representable over a prime field, there exists a constant-competitive matroid secretary algorithm for the matroids in $M$. This result relies on the extremely powerful…
Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number.…
We study the matroid secretary problems with submodular valuation functions. In these problems, the elements arrive in random order. When one element arrives, we have to make an immediate and irrevocable decision on whether to accept it or…
Generalizing a problem posed by Cover, we propose an adversarial game in which a permutation is incrementally constructed in a setting of partial information. As in the secretary problem, this permutation is exposed in stages via the…
We consider probabilistic cloning of a state chosen from a mutually nonorthogonal set of pure states, with the help of a party holding supplementary information in the form of pure states. When the number of states is 2, we show that the…
For a large integer $m,$ we obtain an asymptotic formula for the number of solutions of a certain congruence modulo $m$ with four variables, where the variables belong to special sets of residue classes modulo $m.$ This formula are applied…
One way to interpret the classical secretary problem (CSP) is to consider it as a special case of the following problem. We observe $n$ independent indicator variables $I_1,I_2,\dotsc,I_n$ sequentially and we try to stop on the last…
This paper examines a novel type of multi-agent problem, in which an agent makes multiple identical copies of itself in order to achieve a single agent task better or more efficiently. This strategy improves performance if the environment…
The Matroid Secretary Conjecture is a notorious open problem in online optimization. It claims the existence of an $O(1)$-competitive algorithm for the Matroid Secretary Problem (MSP). Here, the elements of a weighted matroid appear…
Online knapsack problem is considered, where items arrive in a sequential fashion that have two attributes; value and weight. Each arriving item has to be accepted or rejected on its arrival irrevocably. The objective is to maximize the sum…
Online advertising has motivated interest in online selection problems. Displaying ads to the right users benefits both the platform (e.g., via pay-per-click) and the advertisers (by increasing their reach). In practice, not all users click…
The purpose of this paper is to introduce a new numerical method to solve multi-marginal optimal transport problems with pairwise interaction costs. The complexity of multi-marginal optimal transport generally scales exponentially in the…
Motivated by the common academic problem of allocating papers to referees for conference reviewing we propose a novel mechanism for solving the assignment problem when we have a two sided matching problem with preferences from one side (the…
This paper introduces a heuristic framework for the Best Secretary Problem, where one item must be selected using rank information only. We develop five data-responsive rules extending classical fixed-cutoff methods: an expected-record…
In the classic prophet inequality, samples from independent random variables arrive online. A gambler that knows the distributions must decide at each point in time whether to stop and pick the current sample or to continue and lose that…
Suppose a set of requests arrives online: each request gives some value $v_i$ if accepted, but requires using some amount of each of $d$ resources. Our cost is a convex function of the vector of total utilization of these $d$ resources.…
The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of…
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…
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…