Related papers: The Online Submodular Assignment Problem
Constrained $k$-submodular maximization is a general framework that captures many discrete optimization problems such as ad allocation, influence maximization, personalized recommendation, and many others. In many of these applications,…
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this…
In the online bipartite matching with reassignments problem, an algorithm is initially given only one side of the vertex set of a bipartite graph; the vertices on the other side are revealed to the algorithm one by one, along with its…
A matching platform is a system that matches different types of participants, such as companies and job-seekers. In such a platform, merely maximizing the number of matches can result in matches being concentrated on highly popular…
Optimization problems often involve vector norms, which has led to extensive research on developing algorithms that can handle objectives beyond the $\ell_p$ norms. Our work introduces the concept of submodular norms, which are a versatile…
Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize value of information? These applications exhibit strong diminishing returns: Selection of…
The Multidimensional Assignment Problem (MAP or s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s have also a number of…
Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis -- including potential functions and primal-dual techniques -- give insight into this…
Many real-world resource allocation systems, such as humanitarian logistics and vaccine distribution, must preposition limited supply across multiple locations before demand is realized while stockouts incur irreversible service losses. To…
We study the classic online bipartite matching problem with a twist: offline vertices, called resources, are $\textit{reusable}$. In particular, when a resource is matched to an online vertex it is unavailable for a deterministic time…
In the problem of Submodular Max-Min Allocation, we are given a set of items, a set of players, and monotone submodular valuation functions that represent the satisfaction of a player with a certain subset of items. The goal is to find an…
We study the \emph{Submodular Welfare Problem} (SWP), where items are partitioned among agents with monotone submodular utilities to maximize the total welfare under \emph{bandit feedback}. Classical SWP assumes full value-oracle access,…
In the online bipartite matching problem with replacements, all the vertices on one side of the bipartition are given, and the vertices on the other side arrive one by one with all their incident edges. The goal is to maintain a maximum…
We introduce and study spatiotemporal online allocation with deadline constraints ($\mathsf{SOAD}$), a new online problem motivated by emerging challenges in sustainability and energy. In $\mathsf{SOAD}$, an online player completes a…
Online allocation is a broad class of problems where items arriving online have to be allocated to agents who have a fixed utility/cost for each assigned item so to maximize/minimize some objective. This framework captures a broad range of…
We propose a truthful-in-expectation, $(1-1/e)$-approximation mechanism for a strategic variant of the generalized assignment problem (GAP). In GAP, a set of items has to be optimally assigned to a set of bins without exceeding the capacity…
Design of {\it online algorithms} for assigning mobile users to basestations is considered with the objective of maximizing the sum-rate, when all users associated to any one basestation equally share each basestation's resources. Each user…
Matching problems with group-fairness constraints and diversity constraints have numerous applications such as in allocation problems, committee selection, school choice, etc. Moreover, online matching problems have lots of applications in…
In their seminal paper, Karp, Vazirani and Vazirani (STOC'90) introduce the online bipartite matching problem, and the RANKING algorithm, which admits a tight $1-\frac{1}{e}$ competitive ratio. Since its publication, the problem has…
We study the $b$-matching problem in bipartite graphs $G=(S,R,E)$. Each vertex $s\in S$ is a server with individual capacity $b_s$. The vertices $r\in R$ are requests that arrive online and must be assigned instantly to an eligible server.…