Related papers: Tetris with Few Piece Types

The request for high-quality solutions continually grows in a world where more and more tasks are executed through computers. This also counts for fields such as engineering, computer graphics, etc., which use meshes to solve their…

Here we show that deciding whether two rooted binary phylogenetic trees on the same set of taxa permit a cherry-picking sequence, a special type of elimination order on the taxa, is NP-complete. This improves on an earlier result which…

We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds;…

In the Vertex Cover Reconfiguration (VCR) problem, given a graph $G$, positive integers $k$ and $\ell$ and two vertex covers $S$ and $T$ of $G$ of size at most $k$, we determine whether $S$ can be transformed into $T$ by a sequence of at…

We prove that the 2017 puzzle game ZHED is NP-complete, even with just 1 tiles. Such a puzzle is defined by a set of unit-square 1 tiles in a square grid, and a target square of the grid. A move consists of selecting an unselected 1 tile…

We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…

This paper first analyzes the resolution complexity of two random CSP models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into CNF formulas, it…

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…

We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and…

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

Itemset mining is one of the most studied tasks in knowledge discovery. In this paper we analyze the computational complexity of three central itemset mining problems. We prove that mining confident rules with a given item in the head is…

We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete

We prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms…

Let C be a finite set of N elements and R = r_1,r_2,..., r_m a family of M subsets of C. A subset X of R verifies the Consecutive Ones Property (C1P) if there exists a permutation P of C such that each r_i in X is an interval of P. A…

We study the complexity of problems related to subgame-perfect equilibria (SPEs) in infinite duration non zero-sum multiplayer games played on finite graphs with parity objectives. We present new complexity results that close gaps in the…

A graph is called $t$-tough if the removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$ components. The toughness of a graph is the largest $t$ for which the graph is $t$-tough. A graph is minimally $t$-tough if…

Let $t$ be a positive real number. A graph is called $t$-tough if the removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$ components. The toughness of a graph is the largest $t$ for which the graph is $t$-tough.…

One-to-one set matching is a key design for DETR to establish its end-to-end capability, so that object detection does not require a hand-crafted NMS (non-maximum suppression) to remove duplicate detections. This end-to-end signature is…

Characterising tractable fragments of the constraint satisfaction problem (CSP) is an important challenge in theoretical computer science and artificial intelligence. Forbidding patterns (generic sub-instances) provides a means of defining…

Petri games are a multi-player game model for the automatic synthesis of distributed systems, where the players are represented as tokens on a Petri net and are grouped into environment players and system players. As long as the players…