Equivalence of the filament and overlap graphs of subtrees of limited trees

The overlap graphs of subtrees of a tree are equivalent to subtree filament graphs, the overlap graphs of subtrees of a star are cocomparability graphs, and the overlap graphs of subtrees of a caterpillar are interval filament graphs. In this paper, we show the equivalence of many more classes of subtree overlap and subtree filament graphs, and equate them to classes of complements of cochordal-mixed graphs. Our results generalize the previously known results mentioned above

Building a Better Mouse Maze

Mouse Maze is a Flash game about Squeaky, a mouse who has to navigate a subset of the grid using a simple deterministic rule, which naturally generalises to a game on arbitrary graphs with some interesting chaotic dynamics. We present the results of some evolutionary algorithms which generate graphs which effectively trap Squeaky in the maze for long periods of time, and some theoretical results on how long he can be trapped. We then discuss what would happen to Squeaky if he couldn’t count, and present some open problems in the area

Deleting Edges to Restrict the Size of an Epidemic: A New Application for Treewidth

Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most k edges from a given input graph (of small treewidth) so that the maximum component size in the resulting graph is at most h. While this problem is NP-complete in general, we provide evidence that many of the real-world networks of interest are likely to have small treewidth, and we describe an algorithm which solves the problem in time O((wh)2wn) on an input graph having n vertices and whose treewidth is bounded by a fixed constant w

Recognising the overlap graphs of subtrees of restricted trees is hard

The overlap graphs of subtrees in a tree (SOGs) generalise many other graphs classes with set representation characterisations. The complexity of recognising SOGs is open. The complexities of recognising many subclasses of SOGs are known. Weconsider several subclasses of SOGs by restricting the underlying tree. For a fixed integer $k \geq 3$, we consider:\begin{my_itemize} \item The overlap graphs of subtrees in a tree where that tree has $k$ leaves \item The overlap graphs of subtrees in trees that can be derived from a given input tree by subdivision and have at least 3 leaves \item The overlap and intersection graphs of paths in a tree where that tree has maximum degree $k$\end{my_itemize} We show that the recognition problems of these classes are NP-complete. For all other parameters we get circle graphs, well known to be polynomially recognizable

Games on interval and permutation graph representations

We describe combinatorial games on graphs in which two players antagonistically build a representation of a subgraph of a given graph. We show that for a large class of these games, determining whether a given instance is a winning position for the next player is PSPACE-hard. In contrast, we give polynomial time algorithms for solving some versions of the games on trees

A Fast Method for Parallel Document Identification

We present a fast method to identify homogeneous parallel documents. The method is based on collecting counts of identical low-frequency words between possibly parallel documents. The candidate with the most shared low-frequency words is selected as the parallel document. The method achieved 99.96% accuracy when tested on the EUROPARL corpus of parliamentary proceedings, failing only in anomalous cases of truncated or otherwise distorted documents. While other work has shown similar performance on this type of dataset, our approach presented here is faster and does not require training. Apart from proposing an efficient method for parallel document identification in a restricted domain, this paper furnishes evidence that parliamentary proceedings may be inappropriate for testing parallel document identification systems in general

A Fast Method for Parallel Document Identification

We present a fast method to identify homogeneous parallel documents. The method is based on collecting counts of identical low-frequency words between possibly parallel documents. The candidate with the most shared low-frequency words is selected as the parallel document. The method achieved 99.96% accuracy when tested on the EUROPARL corpus of parliamentary proceedings, failing only in anomalous cases of truncated or otherwise distorted documents. While other work has shown similar performance on this type of dataset, our approach presented here is faster and does not require training. Apart from proposing an efficient method for parallel document identification in a restricted domain, this paper furnishes evidence that parliamentary proceedings may be inappropriate for testing parallel document identification systems in general

Recognising the overlap graphs of subtrees of restricted trees is hard

The overlap graphs of subtrees in a tree (SOGs) generalise many other graphs classes with set representation characterisations. The complexity of recognising SOGs is open. The complexities of recognising many subclasses of SOGs are known. Weconsider several subclasses of SOGs by restricting the underlying tree. For a fixed integer $k \geq 3$, we consider:\begin{my_itemize} \item The overlap graphs of subtrees in a tree where that tree has $k$ leaves \item The overlap graphs of subtrees in trees that can be derived from a given input tree by subdivision and have at least 3 leaves \item The overlap and intersection graphs of paths in a tree where that tree has maximum degree $k$\end{my_itemize} We show that the recognition problems of these classes are NP-complete. For all other parameters we get circle graphs, well known to be polynomially recognizable