String problems arise in various applications ranging from text mining to biological sequence analysis. Many string problems are NP-hard. This motivates the search for (fixed-parameter) tractable special cases of these problems. We survey parameterized and multivariate algorithmics results for NP-hard string problems and identify challenges for future research.

In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial. In this paper, two different vulnerability parameters of graphs, tenacity and rupture degree are defined. In general, computing the tenacity o...

We show that the problem of finding a set with maximum cohesion in an undirected network is NP-hard. Key-words: social networks, complex networks, cohesion, np-complete, complexity in ria -0 06 21 06 5, v er si on 2 9 O ct 2 01 1 Maximiser la Cohésion est NP-dur Résumé : Nous montrons que le problème de trouver un ensemble de cohésion maximum dans un graphe non orienté est NP-dur. Mots-clés : r...

A state amalgamation of a directed graph is a node contraction which is only permitted under certain configurations of incident edges. In symbolic dynamics, state amalgamation and its inverse operation, state splitting, play a fundamental role in the the theory of subshifts of finite type (SFT): any conjugacy between SFTs, given as vertex shifts, can be expressed as a sequence of symbol splitti...

We consider only undirected graphs without loops or multiple edges. Our terminology and notation will be standard except as indicated; a good reference for any undefined terms is [2]. We will use c(G) to denote the number of components of a graph G. Chvtital introduced the notion of tough graphs in [3]. Let t be any positive real number. A graph G is said to be t-tough if tc(G-X)5 JXJ for all X...

Given a small polygon S, a big simple polygon B and a positive integer k, it is shown to be NP-hard to determine whether k copies of the small polygon (allowing translation and rotation) can be placed in the big polygon without overlap. Previous NP-hardness results were only known in the case where the big polygon is allowed to be non-simple. A novel reduction from Planar-Circuit-SAT is present...

We prove that a particular pushing-blocks puzzle is intractable in 2D, improving an earlier result that established intractability in 3D [OS99]. The puzzle, inspired by the game PushPush, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only pu...

This lecture focuses on the MAX-E3LIN problem. We prove that approximating it is NP-hard by a reduction from LABEL-COVER. In the MAX-E3LIN problem, our input is a series of linear equations (mod 2) in n binary variables, each with three terms. Equivalently, one can think of this as ±1 variables and ternary products. The objective is to maximize the fraction of satisfied equations.

We prove NP-hardness results for five of Nintendo’s largest video game franchises: Mario, Donkey Kong, Legend of Zelda, Metroid, and Pokémon. Our results apply to Super Mario Bros. 1, 3, Lost Levels, and Super Mario World; Donkey Kong Country 1–3; all Legend of Zelda games except Zelda II: The Adventure of Link; all Metroid games; and all Pokémon role-playing games. For Mario and Donkey Kong, w...

A pool resolution proof is a dag-like resolution proof which admits a depth-first traversal tree in which no variable is used as a resolution variable twice on any branch. The problem of determining whether a given dag-like resolution proof is a valid pool resolution proof is shown to be NP-complete. Propositional resolution has been the foundational method for reasoning in propositional logic,...