Related papers: Complexity and Approximation Algorithms for Fixed …
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…
Reallocation scheduling is one of the most fundamental problems in various areas such as supply chain management, logistics, and transportation science. In this paper, we introduce the reallocation problem that models the scheduling in…
This report provides a comprehensive complexity study of line switching in the Linear DC model for the feasibility problem and the optimization problems of maximizing the load that can be served (maximum switching flow, MSF) and minimizing…
Multimarginal Optimal Transport (MOT) is the problem of linear programming over joint probability distributions with fixed marginals. A key issue in many applications is the complexity of solving MOT: the linear program has exponential size…
In this work, we study a range of constrained versions of the $k$-supplier and $k$-center problems such as: capacitated, fault-tolerant, fair, etc. These problems fall under a broad framework of constrained clustering. A unified framework…
Given a $d$-dimensional continuous (resp. discrete) probability distribution $\mu$ and a discrete distribution $\nu$, the semi-discrete (resp. discrete) Optimal Transport (OT) problem asks for computing a minimum-cost plan to transport mass…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its…
We introduce and study a class of optimization problems we coin replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Nodes with capacity for storing a certain commodity…
Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithms design. While each of them being very active in its own, there is an increasing attention to the connection…
In this work, we provide faster algorithms for approximating the optimal transport distance, e.g. earth mover's distance, between two discrete probability distributions $\mu, \nu \in \Delta^n$. Given a cost function $C : [n] \times [n] \to…
We study the capacitated $k$-facility location problem, in which we are given a set of clients with demands, a set of facilities with capacities and a constant number $k$. It costs $f_i$ to open facility $i$, and $c_{ij}$ for facility $i$…
We present approximation algorithms for several network design problems in the model of Flexible Graph Connectivity (Adjiashvili, Hommelsheim and M\"uhlenthaler, "Flexible Graph Connectivity", Math. Program. pp. 1-33 (2021), and IPCO 2020:…
We consider the capacitated clustering problem in general metric spaces where the goal is to identify $k$ clusters and minimize the sum of the radii of the clusters (we call this the Capacitated-$k$-sumRadii problem). We are interested in…
We study the non-uniform capacitated multi-item lot-sizing (\lotsizing) problem. In this problem, there is a set of demands over a planning horizon of $T$ time periods and all demands must be satisfied on time. We can place an order at the…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
In this paper, we give first constant factor approximation for capacitated knapsack median problem (CKM) for hard uniform capacities, violating the budget only by an additive factor of $f_{max}$ where $f_{max}$ is the maximum cost of a…
Nonlinear programming problems are useful in designing and assigning work schedule and also in transporting goods and services from known sources to specified destinations. The objective function could be linear or nonlinear depending on…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different…