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Large-scale itinerary planning is a variant of the traveling salesman problem, aiming to determine an optimal path that maximizes the collected points of interest (POIs) scores while minimizing travel time and cost, subject to travel…
In the unsplittable capacitated vehicle routing problem (UCVRP) on trees, we are given a rooted tree with edge weights and a subset of vertices of the tree called terminals. Each terminal is associated with a positive demand between 0 and…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
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…
Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…
The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature,…
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
We present a new $(\frac32+\frac1{\mathrm{e}})$-approximation algorithm for the Ordered Traveling Salesperson Problem (Ordered TSP). Ordered TSP is a variant of the classical metric Traveling Salesperson Problem (TSP) where a specified…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two…
We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says…
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp…
We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems. Our approach mainly relies on a novel combination of the classical quadratic penalty, alternating…
In the maximum asymmetric traveling salesman problem (Max ATSP) we are given a complete directed graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. In this paper we give a fast…
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…
We investigate semi-streaming algorithms for the Traveling Salesman Problem (TSP). Specifically, we focus on a variant known as the $(1,2)$-TSP, where the distances between any two vertices are either one or two. Our primary emphasis is on…
Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written…
The Capacitated Vehicle Routing Problem (CVRP) is a core NP-hard problem in the field of combinatorial optimization. It aims to plan optimal routes for a fleet of vehicles with uniform capacity, serving a set of customers with specific…
We propose an implementable, neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric…