Related papers: A Graph Theoretic Additive Approximation of Optima…
We propose a protocol optimization technique that is applicable to both weighted or unweighted graphs. Our aim is to explore by how much a small variation around the Shortest Path or Optimal Path protocols can enhance protocol performance.…
We propose a novel exact algorithm for the transportation problem, one of the paradigmatic network optimization problems. The algorithm, denoted Iterated Inside Out, requires in input a basic feasible solution and is composed by two main…
Solving optimization problems leads to elegant and practical solutions in a wide variety of real-world applications. In many of those real-world applications, some of the information required to specify the relevant optimization problem is…
The optimal transport problem studies how to transport one measure to another in the most cost-effective way and has wide range of applications from economics to machine learning. In this paper, we introduce and study an information…
The Traveling Thief Problem (TTP) is a multi-component optimization problem that captures the interplay between routing and packing decisions by combining the classical Traveling Salesperson Problem (TSP) and the Knapsack Problem (KP). The…
This paper introduces the first statistically consistent estimator of the optimal transport map between two probability distributions, based on neural networks. Building on theoretical and practical advances in the field of Lipschitz neural…
In routing games, agents pick their routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average…
In this paper we investigate the computational complexity of motivating time-inconsistent agents to complete long term projects. We resort to an elegant graph-theoretic model, introduced by Kleinberg and Oren, which consists of a task graph…
In the classical Node-Disjoint Paths (NDP) problem, the input consists of an undirected $n$-vertex graph $G$, and a collection $\mathcal{M}=\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of pairs of its vertices, called source-destination, or demand,…
Several recent applications of optimal transport (OT) theory to machine learning have relied on regularization, notably entropy and the Sinkhorn algorithm. Because matrix-vector products are pervasive in the Sinkhorn algorithm, several…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
Let $G=(V,E,w)$ be a weighted undirected graph with $n$ vertices and $m$ edges, and fix a set of $s$ sources $S\subseteq V$. We study the problem of computing {\em almost shortest paths} (ASP) for all pairs in $S \times V$ in both classical…
The Stacker Crane Problem is NP-Hard and the best known approximation algorithm only provides a 9/5 approximation ratio. The objective of this paper is threefold. First, by embedding the problem within a stochastic framework, we present a…
Realistic path planning applications often require optimizing with respect to several criteria simultaneously. Here we introduce an efficient algorithm for bi-criteria path planning on graphs. Our approach is based on augmenting the state…
We develop new $(1+\epsilon)$-approximation algorithms for finding the global minimum edge-cut in a directed edge-weighted graph, and for finding the global minimum vertex-cut in a directed vertex-weighted graph. Our algorithms are…
The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph $G$ such that we may support insertions and deletions of edges in $G$ as well as distance queries between any two nodes $u,v$ subject to the constraint…
The use of optimal transport (OT) distances, and in particular entropic-regularised OT distances, is an increasingly popular evaluation metric in many areas of machine learning and data science. Their use has largely been driven by the…
Solving point-wise feature correspondence in visual data is a fundamental problem in computer vision. A powerful model that addresses this challenge is to formulate it as graph matching, which entails solving a Quadratic Assignment Problem…
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…
Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community due to its potency and relevance in modeling and machine learning. It introduces means that serve as powerful ways to compare…