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The theory of imprecise Markov chains has achieved significant progress in recent years. Its applicability, however, is still very much limited, due in large part to the lack of efficient computational methods for calculating…
Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints have a general optimal solution, there is increasing demand for parametric…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of…
We study multi-budgeted variants of the classic minimum cut problem and graph separation problems that turned out to be important in parameterized complexity: Skew Multicut and Directed Feedback Arc Set. In our generalization, we assign…
Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied…
Oriented matroids (often called order types) are combinatorial structures that generalize point configurations, vector configurations, hyperplane arrangements, polyhedra, linear programs, and directed graphs. Oriented matroids have played a…
One of the most important questions in matroid optimization is to find disjoint common bases of two matroids. The significance of the problem is well-illustrated by the long list of conjectures that can be formulated as special cases.…
Edge-coloring problems with forbidden patterns are decision problems asking to find an edge-coloring of the input graph which avoids a homomorphism from a fixed forbidden family of edge-colored graphs. In the precolored version of these…
We consider the discrepancy problem of coloring $n$ intervals with $k$ colors such that at each point on the line, the maximal difference between the number of intervals of any two colors is minimal. Somewhat surprisingly, a coloring with…
Vertex colouring is a well-known problem in combinatorial optimisation, whose alternative integer programming formulations have recently attracted considerable attention. This paper briefly surveys seven known formulations of vertex…
Initially developed for the min-knapsack problem, the knapsack cover inequalities are used in the current best relaxations for numerous combinatorial optimization problems of covering type. In spite of their widespread use, these…
Matrix sketching is a recently developed data compression technique. An input matrix A is efficiently approximated with a smaller matrix B, so that B preserves most of the properties of A up to some guaranteed approximation ratio. In so…
In this work we study the polytope associated with a 0/1 integer programming formulation for the Equitable Coloring Problem. We find several families of valid inequalities and derive sufficient conditions in order to be facet-defining…
We introduce $\mathcal{V}$-polyhedral disjunctive cuts (VPCs) for generating valid inequalities from general disjunctions. Cuts are critical to integer programming solvers, but the benefit from many families is only realized when the cuts…
This paper studies Minimum Spanning Trees under incomplete information for its vertices. We assume that no information is available on the precise placement of vertices so that it is only known that vertices belong to some neighborhoods…
We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph $H$ to $n$-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new…
Robust optimization is one of the fundamental approaches to deal with uncertainty in combinatorial optimization. This paper considers the robust spanning tree problem with interval data, which arises in a variety of telecommunication…
We consider upward-planar layered drawings of directed graphs, i.e., crossing-free drawings in which each edge is drawn as a y-monotone curve going upward from its tail to its head, and the y-coordinates of the vertices are integers. The…
We study approaches for the exact solution of the \NP--hard minimum spanning tree problem under conflict constraints. Given a graph $G(V,E)$ and a set $C \subset E \times E$ of conflicting edge pairs, the problem consists of finding a…