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High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering. However, their numerical treatment poses formidable challenges since traditional grid-based methods tend to be frustrated by the…
The quadratic minimum spanning tree problem and its variations such as the quadratic bottleneck spanning tree problem, the minimum spanning tree problem with conflict pair constraints, and the bottleneck spanning tree problem with conflict…
From the 1970s up to now, Mastermind, a classic two-player game, has attracted plenty of attention, not only from the public as a popular game, but also from the academic community as a scientific issue. Mastermind with n positions and k…
We introduce a search game for two players played on a "scenario" consisting of a ground set together with a collection of feasible partitions. This general setting allows us to obtain new characterisations of many width parameters such as…
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…
A query game is a pair of a set $Q$ of queries and a set $\mathcal{F}$ of functions, or codewords $f:Q\rightarrow \mathbb{Z}.$ We think of this as a two-player game. One player, Codemaker, picks a hidden codeword $f\in \mathcal{F}$. The…
In this paper we introduce a new game; in this game there are two players who play as rival pirate gangs. The goal is to gather more treasure than your rival. The game is played on a graph and a player gathers treasure by moving to an…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
We prove PSPACE-hardness for fifteen games in the Super Mario Bros. 2D platforming video game series. Previously, only the original Super Mario Bros. was known to be PSPACE-hard (FUN 2016), though several of the games we study were known to…
While traditionally a labour intensive task, the testing of game content is progressively becoming more automated. Among the many directions in which this automation is taking shape, automatic play-testing is one of the most promising…
The author has long enjoyed using the CSP refinement checker FDR to solve puzzles, as witnessed by examples in \cite{tpc,ucs}. Recent experiments have shown that a number of games of patience (card games for one) are now well within bounds.…
We show that the problem of finding a set with maximum cohesion in an undirected network is NP-hard.
In this paper, we consider the maximum $k$-edge-colorable subgraph problem. In this problem we are given a graph $G$ and a positive integer $k$, the goal is to take $k$ matchings of $G$ such that their union contains maximum number of…
The Parks Puzzle is a paper-and-pencil puzzle game that is classically played on a square grid with different colored regions (the parks). The player needs to place a certain number of "trees" in each row, column, and park such that none…
The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through…
Many problems in compositional synthesis and verification of multi-agent systems -- such as rational verification and assume-guarantee verification in probabilistic systems -- reduce to reasoning about two-player multi-objective stochastic…
We study the complexity of the popular one player combinatorial game known as Flood-It. In this game the player is given an n by n board of tiles where each tile is allocated one of c colours. The goal is to make the colours of all tiles…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and…
Due mostly to its application to cognitive radio networks, multiplayer bandits gained a lot of interest in the last decade. A considerable progress has been made on its theoretical aspect. However, the current algorithms are far from…
We establish some general schemes relating the computational complexity of a video game to the presence of certain common elements or mechanics, such as destroyable paths, collectible items, doors opened by keys or activated by buttons or…