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This paper presents an $O(\log\log \bar{d})$ round massively parallel algorithm for $1+\epsilon$ approximation of maximum weighted $b$-matchings, using near-linear memory per machine. Here $\bar{d}$ denotes the average degree in the graph…
In the Cumulative Vehicle Routing Problem (Cu-VRP), we need to find a feasible itinerary for a capacitated vehicle located at the depot to satisfy customers' demand, as in the well-known Vehicle Routing Problem (VRP), but the goal is to…
Optimization problems consist of either maximizing or minimizing an objective function. Instead of looking for a maximum solution (resp. minimum solution), one can find a minimum maximal solution (resp. maximum minimal solution). Such…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Although many well-known algorithms can solve each bipartite matching problem instance efficiently, it remains an open question how one could estimate the expected optimal matching distance for arbitrary numbers of randomly distributed…
The Capacitated Location Routing Problem is an important planning and routing problem in logistics, which generalizes the capacitated vehicle routing problem and the uncapacitated facility location problem. In this problem, we are given a…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal…
Given an edge-weighted metric complete graph with $n$ vertices, the maximum weight metric triangle packing problem is to find a set of $n/3$ vertex-disjoint triangles with the total weight of all triangles in the packing maximized. Several…
This paper presents an algorithm for estimating the weight of a maximum weighted matching by augmenting any estimation routine for the size of an unweighted matching. The algorithm is implementable in any streaming model including dynamic…
Since the Bin Packing Problem (BPP) is one of the main NP-hard problems, a lot of approximation algorithms have been suggested for it. It has been proven that the best algorithm for BPP has the approximation ratio of 3/2 and the time order…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…
Given two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ over the same ground set, the matroid intersection problem is to find the maximum cardinality common independent set. In the weighted version of the problem, the goal is to find a…
Let G be a bipartite graph with positive integer weights on the edges and without isolated nodes. Let n, N and W be the node count, the largest edge weight and the total weight of G. Let k(x,y) be log(x)/log(x^2/y). We present a new…
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…
We study the problem of computing a minimum equivalent digraph (also known as the problem of computing a strong transitive reduction) and its maximum objective function variant, with two types of extensions. First, we allow to declare a set…
A matching in a graph is a set of edges no two of which share a common vertex. A matching M is an induced matching if no edge connects two edges of M. The problem of finding a maximum induced matching is known to be NP-hard in general and…
We study the problem of finding a \textit{maximal} transitive relation contained in a given binary relation. Given a binary relation of size $m$ defined on a set of size $n$, we present a polynomial time algorithm that finds a maximal…
Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…
We study the complexity of the maximum coverage problem, restricted to set systems of bounded VC-dimension. Our main result is a fixed-parameter tractable approximation scheme: an algorithm that outputs a $(1-\eps)$-approximation to the…