Compact representations of separable graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
High-order entropy-compressed text indexes
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
NC-Algorithms for Graphs with Small Treewidth
WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
All-pairs shortest paths for unweighted undirected graphs in o(mn) time
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Graph Treewidth and Geometric Thickness Parameters
Discrete & Computational Geometry
Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets
ACM Transactions on Algorithms (TALG)
On Compact Representations of All-Pairs-Shortest-Path-Distance Matrices
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Succinct Representations of Arbitrary Graphs
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Shorter implicit representation for planar graphs and bounded treewidth graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Succinct representation of labeled graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Succinct representations of separable graphs
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Succinct ordinal trees based on tree covering
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Exact distance oracles for planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Shortest-path queries for complex networks: exploiting low tree-width outside the core
Proceedings of the 15th International Conference on Extending Database Technology
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Given an unlabeled, unweighted, and undirected graph with n vertices and small (but not necessarily constant) treewidth k, we consider the problem of preprocessing the graph to build space-efficient encodings (oracles) to perform various queries efficiently. We assume the word RAM model where the size of a word is Ω (log n) bits. The first oracle, we present, is the navigation oracle which facilitates primitive navigation operations of adjacency, neighborhood, and degree queries. By way of an enumerate argument, which is of independent interest, we show the space requirement of the oracle is optimal to within lower order terms for all treewidths. The oracle supports the mentioned queries all in constant worst-case time. The second oracle, we present, is an exact distance oracle which facilitates distance queries between any pair of vertices (i.e., an all-pair shortest-path oracle). The space requirement of the oracle is also optimal to within lower order terms. Moreover, the distance queries perform in O(k2 log3 k) time. Particularly, for the class of graphs of our interest, graphs of bounded treewidth (where k is constant), the distances are reported in constant worst-case time.