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Consider an online facility assignment problem where a set of facilities $F = \{ f_1, f_2, f_3, \cdots, f_{|F|} \}$ of equal capacity $l$ is situated on a metric space and customers arrive one by one in an online manner on that space. We…
We study deterministic mechanisms for the two-facility location problem. Given the reported locations of n agents on the real line, such a mechanism specifies where to build the two facilities. The single-facility variant of this problem…
In the facility location problem, the task is to place one or more facilities so as to minimize the sum of the agent costs for accessing their nearest facility. Heretofore, in the strategic version, agent locations have been assumed to be…
In the capacitated $k$-median (\CKM) problem, we are given a set $F$ of facilities, each facility $i \in F$ with a capacity $u_i$, a set $C$ of clients, a metric $d$ over $F \cup C$ and an integer $k$. The goal is to open $k$ facilities in…
We address the problem of locating facilities on the $[0,1]$ interval based on reports from strategic agents. The cost of each agent is her distance to the closest facility, and the global objective is to minimize either the maximum cost of…
In the Submodular Facility Location problem (SFL) we are given a collection of $n$ clients and $m$ facilities in a metric space. A feasible solution consists of an assignment of each client to some facility. For each client, one has to pay…
We study a joint facility location and cost planning problem in a competitive market under random utility maximization (RUM) models. The objective is to locate new facilities and make decisions on the costs (or budgets) to spend on the new…
We present an approach to couple the resolution of Combinatorial Optimization problems with methods from Machine Learning, applied to the single source, capacitated, facility location problem. Our study is framed in the context where a…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
This article presents a matheuristic algorithm for the single-source capacitated facility location problem (SSCFLP) and its variants: SSCFLP with K facilities (SSCKFLP), SSCFLP with contiguous service areas (CFLSAP), and SSCFLP with K…
In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several…
We study the facility location games with candidate locations from a mechanism design perspective. Suppose there are n agents located in a metric space whose locations are their private information, and a group of candidate locations for…
Facility location problems are captivating both from theoretical and practical point of view. In this paper, we study some fundamental facility location problems from the space-efficient perspective. Here the input is considered to be given…
Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any…
We study the extended version of the non-uniform, capacitated facility location problem with multiple fulfilment channels between the facilities and clients, each with their own channel capacities and service cost. Though the problem has…
We give a new randomized LP-rounding 1.725-approximation algorithm for the metric Fault-Tolerant Uncapacitated Facility Location problem. This improves on the previously best known 2.076-approximation algorithm of Swamy & Shmoys. To the…
Given facilities with capacities and clients with penalties and demands, the transportation problem with market choice consists in finding the minimum-cost way to partition the clients into unserved clients, paying the penalties, and into…
Clustering is one of the most fundamental problem in Machine Learning. Researchers in the field often require a lower bound on the size of the clusters to maintain anonymity and upper bound for the ease of analysis. Specifying an optimal…
This article describes a model and an exact solution method for facility location problems with decision-dependent uncertainties. The model allows characterizing the probability distribution of the random elements as a function of the…
We study the $k$-center problem in the context of individual fairness. Let $P$ be a set of $n$ points in a metric space and $r_x$ be the distance between $x \in P$ and its $\lceil n/k \rceil$-th nearest neighbor. The problem asks to…