Related papers: Rikudo is NP-complete
We show that packing axis-aligned unit squares into a simple polygon $P$ is NP-hard, even when $P$ is an orthogonal and orthogonally convex polygon with half-integer coordinates. It has been known since the early 80s that packing unit…
This paper presents a systematic method to solve difficult 9 x 9 Sudoku puzzles by hand. While computer algorithms exist to solve these puzzles, these algorithms are not good for human's to use because they involve too many steps and…
A division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division…
In this paper we demonstrate a method for counting the number of solutions to various logic puzzles. Specifically, we remove all of the "clues" from the puzzle which help the solver to a unique solution, and instead start from an empty…
Many puzzle video games, like Sokoban, involve moving some agent in a maze. The reachable locations are usually apparent for a human player, and the difficulty of the game is mainly related to performing actions on objects, such as pushing…
Consider a problem where we are given a bipartite graph H with vertices arranged on two horizontal lines in the plane, such that the two sets of vertices placed on the two lines form a bipartition of H. We additionally require that H admits…
We introduce a new decision problem, called Packed Interval Covering (PIC) and show that it is NP-complete.
Inspired by a common technique for shuffling a deck of cards on a table without riffling, we continue the study of a prequel paper on the pile shuffle and its capabilities as a sorting device. We study two sort feasibility problems of…
In this paper, we show that deciding rigid foldability of a given crease pattern using all creases is weakly NP-hard by a reduction from Partition, and that deciding rigid foldability with optional creases is strongly NP-hard by a reduction…
The Traveling Tournament Problem is a sports-scheduling problem where the goal is to minimize the total travel distance of teams playing a double round-robin tournament. The constraint 'k' is an imposed upper bound on the number of…
We prove that the classic falling-block video game Tetris (both survival and board clearing) remains NP-complete even when restricted to 8 columns, or to 4 rows, settling open problems posed over 15 years ago [BDH+04]. Our reduction is from…
Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items,…
All roads lead to Rome is the core idea of the puzzle game Roma. It is played on an $n \times n$ grid consisting of quadratic cells. Those cells are grouped into boxes of at most four neighboring cells and are either filled, or to be…
Bingo is played on a $5\times 5$ grid. Take the 25 squares to be the ground set of a closure system in which square $s$ is dependent on a set $S$ of squares iff $s$ completes a line - a row, column, or diagonal - with squares that are…
We explore the capabilities of physical computing with Oscillatory Neural Networks (ONN) to solve combinatorial optimization problems. To solve Sudokus with ONNs, we define a novel mapping strategy that utilizes the unique characteristics…
We provide a simple linear time transformation from a directed or undirected graph with labeled edges to an unlabeled digraph, such that paths in the input graph in which no two consecutive edges have the same label correspond to paths in…
We establish a principle that we call the Fatou-Shishikura injection for Newton maps of polynomials: there is a dynamically natural injection from the set of non-repelling periodic orbits of any Newton map to the set of its critical orbits.…
The clique number of a tournament is the maximum clique number of a graph formed by keeping backwards arcs in an ordering of its vertices. We study the time complexity of computing the clique number of a tournament and prove that, for any…
This paper investigates the popular card game UNO from the viewpoint of algorithmic combinatorial game theory. We define simple and concise mathematical models for the game, including both cooperative and uncooperative versions, and analyze…
The rules of Sudoku are often specified using twenty seven \texttt{all\_different} constraints, referred to as the {\em big} \mrules. Using graphical proofs and exploratory logic programming, the following main and new result is obtained:…