Related papers: Constant-Competitiveness for Random Assignment Mat…
We consider matroid allocation problems under opportunity fairness constraints: resources need to be allocated to a set of agents under matroid constraints (which include classical problems such as bipartite matching). Agents are divided…
There is a rising interest for studying the online benchmark as an alternative of the classical offline benchmark in online stochastic settings. Ezra, Feldman, Gravin, and Tang (SODA 2023) introduced the notion of order-competitive ratio,…
We study random order semi-streaming algorithms for submodular maximization under a wide range of combinatorial constraint classes, including matroids, matroid $p$-parity, $p$-exchange systems and $p$-systems. For most of these classes of…
The $b$-matching problem is an allocation problem where the vertices on the left-hand side of a bipartite graph, referred to as servers, may be matched multiple times. In the setting with stochastic rewards, an assignment between an…
Algorithm designers typically assume that the input data is correct, and then proceed to find "optimal" or "sub-optimal" solutions using this input data. However this assumption of correct data does not always hold in practice, especially…
The well-known secretary problem in sequential analysis and optimal stopping theory asks one to maximize the probability of finding the optimal candidate in a sequentially examined list under the constraint that accept/reject decisions are…
In the weighted bipartite matching problem, the goal is to find a maximum-weight matching in a bipartite graph with nonnegative edge weights. We consider its online version where the first vertex set is known beforehand, but vertices of the…
We propose a model for recoverable robust optimization with commitment. Given a combinatorial optimization problem and uncertainty about elements that may fail, we ask for a robust solution that, after the failing elements are revealed, can…
We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitive-ratio approximation schemes. Such a scheme algorithmically constructs an online algorithm with a competitive ratio…
We consider the online vector packing problem in which we have a $d$ dimensional knapsack and items $u$ with weight vectors $\mathbf{w}_u \in \mathbb{R}_+^d$ arrive online in an arbitrary order. Upon the arrival of an item, the algorithm…
We study the Monotone Sliding Reconfiguration (MSR) problem, in which $\textit{labeled}$ pairwise interior-disjoint objects in a planar workspace need to be brought $\textit{one by one}$ from their initial positions to given target…
A growing body of work in economics and computation focuses on the trade-off between implementability and simplicity in mechanism design. The goal is to develop a theory that not only allows to design an incentive structure easy to grasp…
This dissertation presents new results on three different themes all related to matroid polytopes. First we investigate properties of Ehrhart polynomials of matroid polytopes, independence matroid polytopes, and polymatroids. We prove that…
Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…
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…
We investigate the problem of fairly allocating $m$ indivisible items among $n$ sequentially arriving agents with additive valuations, under the sought-after fairness notion of maximin share (MMS). We first observe a strong impossibility:…
In the online metric matching problem, $n$ servers and $n$ requests lie in a metric space. Servers are available upfront, and requests arrive sequentially. An arriving request must be matched immediately and irrevocably to an available…
We consider the problem of online scheduling on a single machine in order to minimize weighted flow time. The existing algorithms for this problem (STOC '01, SODA '03, FOCS '18) all require exact knowledge of the processing time of each…
We extend rank-constrained optimization to general hyperbolic programs (HP) using the notion of matroid rank. For LP and SDP respectively, this reduces to sparsity-constrained LP and rank-constrained SDP that are already well-studied. But…
We consider the classical online scheduling problem P||C_{max} in which jobs are released over list and provide a nearly optimal online algorithm. More precisely, an online algorithm whose competitive ratio is at most (1+\epsilon) times…