Related papers: The Minimum Feasible Tileset problem
We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…
In the field of algorithmic self-assembly, a long-standing unproven conjecture has been that of the NP-hardness of binary pattern tile set synthesis (2-PATS). The $k$-PATS problem is that of designing a tile assembly system with the…
We study a combinatorial problem called Minimum Maximal Matching, where we are asked to find in a general graph the smallest that can not be extended. We show that this problem is hard to approximate with a constant smaller than 2, assuming…
In multistage perfect matching problems we are given a sequence of graphs on the same vertex set and asked to find a sequence of perfect matchings, corresponding to the sequence of graphs, such that consecutive matchings are as similar as…
We consider the \emph{smallest superpolyomino problem}: given a set of colored polyominoes, find the smallest polyomino containing each input polyomino as a subshape. This problem is shown to be NP-hard, even when restricted to a set of…
A metro-line crossing minimization problem is to draw multiple lines on an underlying graph that models stations and rail tracks so that the number of crossings of lines becomes minimum. It has several variations by adding restrictions on…
Given a linear system, we consider the problem of finding a small set of variables to affect with an input so that the resulting system is controllable. We show that this problem is NP-hard; indeed, we show that even approximating the…
We consider the Minimum Convex Partition problem: Given a set P of n points in the plane, draw a plane graph G on P, with positive minimum degree, such that G partitions the convex hull of P into a minimum number of convex faces. We show…
We study parameterized approximability of three optimization problems related to stable matching: (1) Min-BP-SMI: Given a stable marriage instance and a number k, find a size-at-least-k matching that minimizes the number $\beta$ of blocking…
The problem that we consider is the following: given an $n \times n$ array $A$ of positive numbers, find a tiling using at most $p$ rectangles (which means that each array element must be covered by some rectangle and no two rectangles must…
In Terminal Monitoring Set (TMS), the input is an undirected graph $G=(V,E)$, together with a collection $T$ of terminal pairs and the goal is to find a subset $S$ of minimum size that hits a shortest path between every pair of terminals.…
In this paper, we study the problem of determining a minimum state probabilistic finite state machine capable of generating statistically identical symbol sequences to samples provided. This problem is qualitatively similar to the classical…
We consider the SUBSET SUM problem and its important variants in this paper. In the SUBSET SUM problem, a (multi-)set $X$ of $n$ positive numbers and a target number $t$ are given, and the task is to find a subset of $X$ with the maximal…
In this paper, we study an NP-hard problem of a single machine scheduling minimizing the makespan, where the mixed-critical tasks with an uncertain processing time are scheduled. We show the derivation of F-shaped tasks from the probability…
We study the following combinatorial problem. Given a set of $n$ y-monotone \emph{wires}, a \emph{tangle} determines the order of the wires on a number of horizontal \emph{layers} such that the orders of the wires on any two consecutive…
We investigate the existence of approximation algorithms for maximization of submodular functions, that run in fixed parameter tractable (FPT) time. Given a non-decreasing submodular set function $v: 2^X \to \mathbb{R}$ the goal is to…
Motivated by group-project distribution, we introduce and study stable matching under the constraint of applicants needing to share a location to be matched with the same institute, which we call the Location-Restricted Stable Matching…
The stable roommates problem can admit multiple different stable matchings. We have different criteria for deciding which one is optimal, but computing those is often NP-hard. We show that the problem of finding generous or rank-maximal…
In the stable marriage and roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually accepted agents. If any…
Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…