Related papers: The Minimum Feasible Tileset problem
The minimum sum coloring problem with bundles was introduced by Darbouy and Friggstad (SWAT 2024) as a common generalization of the minimum coloring problem and the minimum sum coloring problem. During their presentation, the following open…
We consider the Min-$r$-Lin$(Z_m)$ problem: given a system $S$ of length-$r$ linear equations modulo $m$, find $Z \subseteq S$ of minimum cardinality such that $S-Z$ is satisfiable. The problem is NP-hard and UGC-hard to approximate in…
In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
Three well-studied types of subgraph-restricted matchings are induced matchings, uniquely restricted matchings, and acyclic matchings. While it is hard to determine the maximum size of a matching of each of these types, whether some given…
We consider the problem of scheduling $n$ jobs to minimize the makespan on $m$ unrelated machines, where job $j$ requires time $p_{ij}$ if processed on machine $i$. A classic algorithm of Lenstra et al. yields the best known approximation…
Given a set of points in the plane, the \textsc{General Position Subset Selection} problem is that of finding a maximum-size subset of points in general position, i.e., with no three points collinear. The problem is known to be ${\rm…
We consider the complexity of problems related to the combinatorial game Free-Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. Although computing the minimum…
The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for…
The stable marriage and stable roommates problems have been extensively studied due to their high applicability in various real-world scenarios. However, it might happen that no stable solution exists, or stable solutions do not meet…
We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…
For a positive integer $t$ and a graph $G$, an additive $t$-spanner of $G$ is a spanning subgraph in which the distance between every pair of vertices is at most the original distance plus $t$. Minimum Additive $t$-Spanner Problem is to…
Given a graph $G=(V,E)$ with $V=\{1,\ldots,n\}$, we place on every vertex a token $T_1,\ldots,T_n$. A swap is an exchange of tokens on adjacent vertices. We consider the algorithmic question of finding a shortest sequence of swaps such that…
An unconstrained nonlinear binary optimization problem of selecting a maximum expected value subset of items is considered. Each item is associated with a profit and probability. Each of the items succeeds or fails independently with the…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
This investigation studies the decidability problem of plane edge coloring with three symbols. In the edge coloring (or Wang tiles) of a plane, unit squares with colored edges that have one of $p$ colors are arranged side by side such that…
The NP-hard Minimum Common String Partition problem asks whether two strings $x$ and $y$ can each be partitioned into at most $k$ substrings, called blocks, such that both partitions use exactly the same blocks in a different order. We…
The problem of column subset selection asks for a subset of columns from an input matrix such that the matrix can be reconstructed as accurately as possible within the span of the selected columns. A natural extension is to consider a…
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…
Our work is motivated by the challenges presented in preparing arrays of atoms for use in quantum simulation. The recently-developed process of loading atoms into traps results in approximately half of the traps being filled. To consolidate…