Related papers: Technical Note: Split Algorithm in O(n) for the Ca…
The minimum conductance problem is an NP-hard graph partitioning problem. Apart from the search for bottlenecks in complex networks, the problem is very closely related to the popular area of network community detection. In this paper, we…
The capacitated vehicle routing problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. In this problem, we are given a depot and a set of customers, each with a demand, embedded in a metric space. The…
We present a distributed randomized algorithm finding Minimum Spanning Tree (MST) of a given graph in O(1) rounds, with high probability, in the Congested Clique model. The input graph in the Congested Clique model is a graph of n nodes,…
We present a two-level decomposition strategy for solving the Vehicle Routing Problem (VRP) using the Quantum Approximate Optimization Algorithm. A Problem-Level Decomposition partitions a 13-node (156-qubit) VRP into smaller Traveling…
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…
Given a set of messages to be transmitted in packages from a set of sending stations to a set of receiving stations, we are required to schedule the packages so as to achieve the minimum possible time from the moment the 1st transmission…
We study the Multiple Cluster Scheduling problem and the Multiple Strip Packing problem. For both problems, there is no algorithm with approximation ratio better than $2$ unless $P = NP$. In this paper, we present an algorithm with…
Graph partitioning schedules parallel calculations like sparse matrix-vector multiply (SpMV). We consider contiguous partitions, where the $m$ rows (or columns) of a sparse matrix with $N$ nonzeros are split into $K$ parts without…
We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…
Graph neural networks (GNNs), an emerging class of machine learning models for graphs, have gained popularity for their superior performance in various graph analytical tasks. Mini-batch training is commonly used to train GNNs on large…
In this letter, we propose a new routing strategy to improve the transportation efficiency on complex networks. Instead of using the routing strategy for shortest path, we give a generalized routing algorithm to find the so-called {\it…
The bipartite graph structure has shown its promising ability in facilitating the subspace clustering and spectral clustering algorithms for large-scale datasets. To avoid the post-processing via k-means during the bipartite graph…
The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly…
This paper proposes multiple extensions to the popular bicriterion transit routing approach -- Trip-Based Transit Routing (TBTR). Specifically, building on the premise of the HypRAPTOR algorithm, we first extend TBTR to its partitioning…
This paper proposes a quantum algorithm for the capacitated vehicle routing problem with time windows (CVRPTW) based on Grover Search framework. This problem is often faced by Postal services in the context of package delivery or other…
This paper addresses a new variant of the multi-trip single vehicle routing problem where the nodes are related to each other through AND-type precedence constraints. The problem aims at determining a sequence of trips to visit all the…
This article reviews the use of first order convex optimization schemes to solve the discretized dynamic optimal transport problem, initially proposed by Benamou and Brenier. We develop a staggered grid discretization that is well adapted…
The Team Orienteering Problem (TOP) is an attractive variant of the Vehicle Routing Problem (VRP). The aim is to select customers and at the same time organize the visits for a vehicle fleet so as to maximize the collected profits and…
In this paper, we consider the optimal coordination of automated vehicles at intersections under fixed crossing orders. We formulate the problem using direct optimal control and exploit the structure to construct a semi-distributed…
In this paper, we present Approximation Schemes for Capacitated Vehicle Routing Problem (CVRP) on several classes of graphs. In CVRP, introduced by Dantzig and Ramser (1959), we are given a graph $G=(V,E)$ with metric edges costs, a depot…