Related papers: Robust Algorithms for the Secretary Problem
The Bin Packing Problem involves efficiently packing items into a limited number of bins without exceeding their capacity. In this paper, we try to answer a specific question in this field. Mathematically the combinatorial optimization…
We study ordinal approximation algorithms for maximum-weight bipartite matchings. Such algorithms only know the ordinal preferences of the agents/nodes in the graph for their preferred matches, but must compete with fully omniscient…
This paper studies the multi-item newsvendor problem with a constrained budget and information about demand limited to its range, mean and mean absolute deviation. We consider a minimax model that determines order quantities by minimizing…
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…
In this paper we consider the online Submodular Welfare (SW) problem. In this problem we are given $n$ bidders each equipped with a general (not necessarily monotone) submodular utility and $m$ items that arrive online. The goal is to…
We study Matching and other related problems in a partial information setting where the agents' utilities for being matched to other agents are hidden and the mechanism only has access to ordinal preference information. Our model is…
The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total…
We study the success probability for a variant of the secretary problem, with noisy observations and multiple offline selection. Our formulation emulates, and is motivated by, problems involving noisy selection arising in the disciplines of…
Imagine a large firm with multiple departments that plans a large recruitment. Candidates arrive one-by-one, and for each candidate the firm decides, based on her data (CV, skills, experience, etc), whether to summon her for an interview.…
A natural variant of the classical online $k$-server problem is the Weighted $k$-server problem, where the cost of moving a server is its weight times the distance through which it moves. Despite its apparent simplicity, the weighted…
We study the problem of fair $k$-committee selection under an egalitarian objective. Given $n$ agents partitioned into $m$ groups (\eg, demographic quotas), the goal is to aggregate their preferences to form a committee of size $k$ that…
The prospect of finding love may be scary but the prospect of committing to a relationship for the rest of your life is almost certainly scary. The secretary problem is a parallel to romantic decision making where an individual decides when…
Many combinatorial problems involve determining whether a universe of $n$ elements contains a witness consisting of $k$ elements which have some specified property. In this paper we investigate the relationship between the decision and…
We study the stable marriage problem in the partial information setting where the agents, although they have an underlying true strict linear order, are allowed to specify partial orders. Specifically, we focus on the case where the agents…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost…
In resource allocation, we often require that the output allocation of an algorithm is stable against input perturbation because frequent reallocation is costly and untrustworthy. Varma and Yoshida (SODA'21) formalized this requirement for…
We consider Online Minimum Bipartite Matching under the uniform metric. We show that Randomized Greedy achieves a competitive ratio equal to $(1+1/n) (H_{n+1}-1)$, which matches the lower bound. Comparing with the fact that RG achieves an…
We study online multidimensional variants of the generalized assignment problem which are used to model prominent real-world applications, such as the assignment of virtual machines with multiple resource requirements to physical…
We study the problem of matching agents who arrive at a marketplace over time and leave after d time periods. Agents can only be matched while they are present in the marketplace. Each pair of agents can yield a different match value, and…