Related papers: Towards Optimal Running Times for Optimal Transpor…
We present a centralized algorithmic framework for solving multi-robot path planning problems in general, two-dimensional, continuous environments while minimizing globally the task completion time. The framework obtains high levels of…
The {\em maximum cardinality} and {\em maximum weight matching} problems can be solved in time $\tilde{O}(m\sqrt{n})$, a bound that has resisted improvement despite decades of research. (Here $m$ and $n$ are the number of edges and…
For two multisets $S$ and $T$ of points in $[\Delta]^2$, such that $|S| = |T|= n$, the earth-mover distance (EMD) between $S$ and $T$ is the minimum cost of a perfect bipartite matching with edges between points in $S$ and $T$, i.e.,…
We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a * b rectangles such that the sum of the weights of the points in P…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
Optimal transport distances have become a classic tool to compare probability distributions and have found many applications in machine learning. Yet, despite recent algorithmic developments, their complexity prevents their direct use on…
We study the convergence of the transport plans $\gamma_\epsilon$ towards $\gamma_0$ as well as the cost of the entropy-regularized optimal transport $(c,\gamma_\epsilon)$ towards $(c,\gamma_0)$ as the regularization parameter $\epsilon$…
Makespan scheduling on identical machines is one of the most basic and fundamental packing problems studied in the discrete optimization literature. It asks for an assignment of $n$ jobs to a set of $m$ identical machines that minimizes the…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
We present two randomised approximate counting algorithms with $\widetilde{O}(n^{2-c}/\varepsilon^2)$ running time for some constant $c>0$ and accuracy $\varepsilon$: (1) for the hard-core model with fugacity $\lambda$ on graphs with…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
In this paper, we obtain a number of new simple pseudo-polynomial time algorithms on the well-known knapsack problem, focusing on the running time dependency on the number of items $n$, the maximum item weight $w_\mathrm{max}$, and the…
The girth of a graph, i.e. the length of its shortest cycle, is a fundamental graph parameter. Unfortunately all known algorithms for computing, even approximately, the girth and girth-related structures in directed weighted $m$-edge and…
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology…
We give new sublinear and parallel algorithms for the extensively studied problem of approximating n-variable r-CSPs (constraint satisfaction problems with constraints of arity r up to an additive error. The running time of our algorithms…
Given a graph $G = (V, E)$, we wish to compute a spanning tree whose maximum vertex degree, i.e. tree degree, is as small as possible. Computing the exact optimal solution is known to be NP-hard, since it generalizes the Hamiltonian path…
Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we…