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A Hamiltonian decomposition of a regular graph is a partition of its edge set into Hamiltonian cycles. The problem of finding edge-disjoint Hamiltonian cycles in a given regular graph has many applications in combinatorial optimization and…
We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multi-class node classification problem and utilize an unsupervised training strategy based on the statistical physics…
The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to…
Given an unlabeled road map, we consider, from an algorithmic perspective, the cartographic problem to place non-overlapping road labels embedded in their roads. We first decompose the road network into logically coherent road sections,…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…
The aim of this paper is to provide a review of structural decomposition methods in discrete optimization and to give a unified framework in the form of local elimination algorithms (LEA). This paper is organized as follows. Local…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…
The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…
We present a distributed anytime algorithm for performing MAP inference in graphical models. The problem is formulated as a linear programming relaxation over the edges of a graph. The resulting program has a constraint structure that…
We present a factor $14D^2$ approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where $D$ is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time…
Data association across frames is at the core of Multiple Object Tracking (MOT) task. This problem is usually solved by a traditional graph-based optimization or directly learned via deep learning. Despite their popularity, we find some…
An optimization problem is at the heart of many robotics estimating, planning, and optimum control problems. Several attempts have been made at model-based multi-robot localization, and few have formulated the multi-robot collaborative…
Graph alignment refers to the problem of finding a bijective mapping across vertices of two graphs such that, if two nodes are connected in the first graph, their images are connected in the second graph. This problem arises in many fields…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
With the widespread use of shared-nothing clusters of servers, there has been a proliferation of distributed object stores that offer high availability, reliability and enhanced performance for MapReduce-style workloads. However, relational…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…