Theoretical Computer Science
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
On minimizing width in linear layouts
Discrete Applied Mathematics
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
The vertex separation and search number of a graph
Information and Computation
ACM SIGACT News
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Improved approximation algorithms for minimum-weight vertex separators
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Efficient approximation for triangulation of minimum treewidth
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Distributed chasing of network intruders
Theoretical Computer Science
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Monotonicity of non-deterministic graph searching
Theoretical Computer Science
Monotony properties of connected visible graph searching
Information and Computation
Quiescence of self-stabilizing gossiping among mobile agents in graphs
Theoretical Computer Science
Graph searching in a crime wave
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Monotonicity of non-deterministic graph searching
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
On the self-stabilization of mobile robots in graphs
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Distributed chasing of network intruders
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
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We introduce nondeterministic graph searching with a controlled amount of nondeterminism and show how this new tool can be used in algorithm design and combinatorial analysis applying to both pathwidth and treewidth. We prove equivalence between this game- theoretic approach and graph decompositions called q-branched tree decompositions, which can be interpreted as a parameterized version of tree decompositions. Path decomposition and (standard) tree decomposition are two extreme cases of q-branched tree decompositions. The equivalence between nondeterministic graph searching and q-branched tree decomposition enables us to design an exact (exponential time) algorithm computing q-branched treewidth for all q ≥ 0, which is thus valid for both treewidth and pathwidth. This algorithm performs as fast as the best known exact algorithm for pathwidth. Conversely, this equivalence also enables us to design a lower bound on the amount of nondeterminism required to search a graph with the minimum number of searchers.