Related papers: The Min-Cost Matching with Concave Delays Problem
Important pricing problems in centralized matching markets -- such as carpooling, food delivery and freight shipping platforms -- often exhibit a bi-level structure. At the upper level, the platform sets prices for heterogeneous demand…
We introduce a natural online allocation problem that connects several of the most fundamental problems in online optimization. Let $M$ be an $n$-point metric space. Consider a resource that can be allocated in arbitrary fractions to the…
We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists…
We consider an online matching problem with concave returns. This problem is a significant generalization of the Adwords allocation problem and has vast applications in online advertising. In this problem, a sequence of items arrive…
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…
A speed scaling problem is considered, where time is divided into slots, and jobs with payoff $v$ arrive at the beginning of the slot with associated deadlines $d$. Each job takes one slot to be processed, and multiple jobs can be processed…
We study the online convex covering problem and online convex packing problem. The (offline) convex covering problem is modeled by the following convex program: $\min_{x \in R_+^n} f(x) \ \text{s.t}\ A x \ge 1$, where $f : R_+^n \mapsto…
We study a resource allocation problem over time, where a finite (random) resource needs to be distributed among a set of users at each time instant. Shortfalls in the resource allocated result in user dissatisfaction, which we model as an…
In this article, we consider the problem of unconstrained time-varying convex optimization, where the cost function changes with time. We provide an in-depth technical analysis of the problem and argue why freezing the cost at each time…
An algorithm is presented which produces the minimum cost bipartite matching between two sets of M points each, where the cost of matching two points is proportional to the minimum distance by which a particle could reach one point from the…
In this paper, we introduce the online service with delay problem. In this problem, there are $n$ points in a metric space that issue service requests over time, and a server that serves these requests. The goal is to minimize the sum of…
We consider the online minimum cost matching problem on the line, in which there are $n$ servers and, at each of $n$ time steps, a request arrives and must be irrevocably matched to a server that has not yet been matched to, with the goal…
Motivated by applications where a system must remain operational via continual procurement of contracts, we study two online contract selection problems under uncertain prices. At each time step, a price drawn from a known distribution is…
In this paper, we present a framework used to construct and analyze algorithms for online optimization problems with deadlines or with delay over a metric space. Using this framework, we present algorithms for several different problems. We…
We introduce and study a family of online metric problems with long-term constraints. In these problems, an online player makes decisions $\mathbf{x}_t$ in a metric space $(X,d)$ to simultaneously minimize their hitting cost…
Matching platforms, from ridesharing to food delivery to competitive gaming, face a fundamental operational dilemma: match agents immediately to minimize waiting costs, or delay to exploit the efficiency gains of thicker markets. Yet…
We present a new unified framework for minimizing congestion-dependent network cost in information-centric networks by jointly optimizing forwarding and caching strategies. As caching variables are integer-constrained, the resulting…
This paper proposes a set of novel optimization algorithms for solving a class of convex optimization problems with time-varying streaming cost function. We develop an approach to track the optimal solution with a bounded error. Unlike the…
We discuss the optimal matching solution for both the assignment problem and the matching problem in one dimension for a large class of convex cost functions. We consider the problem in a compact set with the topology both of the interval…
Online optimization problems arise in many resource allocation tasks, where the future demands for each resource and the associated utility functions change over time and are not known apriori, yet resources need to be allocated at every…