Related papers: The difficulty of beating the Taxman
In this paper we study a max-min $k$-partition problem on a weighted graph, that could model a robust $k$-coalition formation. We settle the computational complexity of this problem as complete for class $\Sigma_2^P$. This hardness holds…
Grassmann and flag varieties lead many lives in pure and applied mathematics. Here we focus on the algebraic complexity of solving various problems in linear algebra and statistics as optimization problems over these varieties. The measure…
Solving parity games is a major building block for numerous applications in reactive program verification and synthesis. While they can be solved efficiently in practice, no known approach has a polynomial worst-case runtime complexity. We…
We consider a pursuit-evasion game that describes the process of extinguishing a fire burning on the nodes of an undirected graph. We denote the minimum number of firefighters required by ffn(G) and provide almost sharp bounds to this graph…
Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming results need to be developed. This motivation leads us to…
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 a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
This paper discusses the complexity of graph pebbling, dealing with both traditional pebbling and the recently introduced game of cover pebbling. Determining whether a configuration is solvable according to either the traditional definition…
While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and…
Most people struggle with prioritizing work. While inexact heuristics have been developed over time, there is still no tractable principled algorithm for deciding which of the many possible tasks one should tackle in any given day, month,…
The maximum traveling salesman problem (Max~TSP) consists of finding a Hamiltonian cycle with the maximum total weight of the edges in a given complete weighted graph. We prove that, in the case when the edge weights are induced by a metric…
We consider the Travelling Salesman Problem with Vertex Requisitions, where for each position of the tour at most two possible vertices are given. It is known that the problem is strongly NP-hard. The proposed algorithm for this problem has…
Roughly speaking, gerrymandering is the systematic manipulation of the boundaries of electoral districts to make a specific (political) party win as many districts as possible. While typically studied from a geographical point of view,…
Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world…
Many popular puzzle and matching games have been analyzed through the lens of computational complexity. Prominent examples include Sudoku, Candy Crush, and Flood-It. A common theme among these widely played games is that their generalized…
We prove new theoretical results about several variations of the cop and robber game on graphs. First, we consider a variation of the cop and robber game which is more symmetric called the cop and killer game. We prove for all $c < 1$ that…
The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…
Tablut is a complete-knowledge, deterministic, and asymmetric board game, which has not been solved nor properly studied yet. In this work, its rules and characteristics are presented, then a study on its complexity is reported. An upper…
Voting theory has become increasingly integrated with computational social choice and multiagent systems. Computational complexity has been extensively used as a shield against manipulation of voting systems, however for several voting…