Related papers: Graph Profiling for Vertex Cover: Targeted Reducti…
This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
A/B testing is an effective way to assess the potential impacts of two treatments. For A/B tests conducted by IT companies, the test users of A/B testing are often connected and form a social network. The responses of A/B testing can be…
Treewidth is a useful tool in designing graph algorithms. Although many NP-hard graph problems can be solved in linear time when the input graphs have small treewidth, there are problems which remain hard on graphs of bounded treewidth. In…
Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI,…
The graph coloring problem is a classical combinatorial optimization problem with important applications such as register allocation and task scheduling, and it has been extensively studied for decades. However, near-real-time algorithms…
Graph Neural Networks (GNNs) have emerged as a dominant paradigm for learning on graph-structured data, thanks to their ability to jointly exploit node features and relational information encoded in the graph topology. This joint modeling,…
In the Travelling Salesman Problem, every vertex of an edge-weighted graph has to be visited by an agent who traverses the edges of the graph. In this problem, it is usually assumed that the costs of each edge are given in advance, making…
Finding small vertex covers in a graph has applications in numerous domains. Two common formulations of the problem include: Minimum Vertex Cover, which finds the smallest vertex cover in a graph, and Parameterized Vertex Cover, which finds…
We study the problem of prediction for evolving graph data. We formulate the problem as the minimization of a convex objective encouraging sparsity and low-rank of the solution, that reflect natural graph properties. The convex formulation…
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a…
We consider range minimization problems featuring exponentially many variables, as frequently arising in fairness-oriented or bi-objective optimization. While branch and price is successful at solving cost-oriented problems with many…
Many combinatorial problems can be solved in time $O^*(c^{tw})$ on graphs of treewidth $tw$, for a problem-specific constant $c$. In several cases, matching upper and lower bounds on $c$ are known based on the Strong Exponential Time…
Using physical layer network coding, compute-and-forward is a promising relaying scheme that effectively exploits the interference between users and thus achieves high rates. In this paper, we consider the problem of finding the optimal…
We present BiqBin, an exact solver for linearly constrained binary quadratic problems. Our approach is based on an exact penalty method to first efficiently transform the original problem into an instance of Max-Cut, and then to solve the…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
A powerful technique for solving combinatorial optimization problems is to reduce the search space without compromising the solution quality by exploring intrinsic mathematical properties of the problems. For the maximum weight independent…
Finding the stability number of a graph, i.e., the maximum number of vertices of which no two are adjacent, is a well known NP-hard combinatorial optimization problem. Since this problem has several applications in real life, there is need…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
The Graph Burning Problem (GBP) is a combinatorial optimization problem that has gained relevance as a tool for quantifying a graph's vulnerability to contagion. Although it is based on a very simple propagation model, its decision version…