Related papers: The Minimum Feasible Tileset problem
This paper studies a combinatorial optimization problem which is obtained by combining the flow shop scheduling problem and the shortest path problem. The objective of the obtained problem is to select a subset of jobs that constitutes a…
In the Maximum Independent Set problem we are asked to find a set of pairwise nonadjacent vertices in a given graph with the maximum possible cardinality. In general graphs, this classical problem is known to be NP-hard and hard to…
The Steiner Multicycle problem consists of, given a complete graph, a weight function on its vertices, and a collection of pairwise disjoint non-unitary sets called terminal sets, finding a minimum weight collection of vertex-disjoint…
The synthesis problem asks to construct a reactive finite-state system from an $\omega$-regular specification. Initial specifications are often unrealizable, which means that there is no system that implements the specification. A common…
We consider the Minimum Coverage Kernel problem: given a set $B$ of $d$-dimensional boxes, find a subset of $B$ of minimum size covering the same region as $B$. This problem is $\mathsf{NP}$-hard, but as for many $\mathsf{NP}$-hard problems…
We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy $\epsilon$ the Pareto curve of a multiobjective optimization problem. We show that for a broad class of bi-objective problems…
The problem of rectangle tiling binary arrays is defined as follows. Given an $n \times n$ array $A$ of zeros and ones and a natural number $p$, our task is to partition $A$ into at most $p$ rectangular tiles, so that the maximal weight of…
State minimization of combinatorial filters is a fundamental problem that arises, for example, in building cheap, resource-efficient robots. But exact minimization is known to be NP-hard. This paper conducts a more nuanced analysis of this…
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.…
In the Minimum Bisection problem, input is a graph $G$ and the goal is to partition the vertex set into two parts $A$ and $B$, such that $||A|-|B|| \le 1$ and the number $k$ of edges between $A$ and $B$ is minimized. This problem can be…
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…
Discrete tomography deals with reconstructing finite spatial objects from lower dimensional projections and has applications for example in timetable design. In this paper we consider the problem of reconstructing a tile packing from its…
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range…
Scheduling problems are fundamental in combinatorial optimization. Much work has been done on approximation algorithms for NP-hard cases, but relatively little is known about exact solutions when some part of the input is a fixed parameter.…
Many real-world networks can be modeled as graphs. Finding dense subgraphs is a key problem in graph mining with applications in diverse domains. In this paper, we consider two variants of the densest subgraph problem where multiple graph…
Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to…
Finding the largest cardinality feasible subset of an infeasible set of linear constraints is the Maximum Feasible Subsystem problem (MAX FS). Solving this problem is crucial in a wide range of applications such as machine learning and…
We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route $p$ paths from a start vertex to a target vertex in a given graph while using at most $k$ edges more than once. We show that MSE can…
Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…
We study the token swapping problem, in which we are given a graph with an initial assignment of one distinct token to each vertex, and a final desired assignment (again with one token per vertex). The goal is to find the minimum length…