Locality of queries definable in invariant first-order logic with arbitrary built-in predicates
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Dominating set is fixed parameter tractable in claw-free graphs
Theoretical Computer Science
Linear kernels for (connected) dominating set on H-minor-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Parameterized complexity of generalized domination problems
Discrete Applied Mathematics
Structure theorem and isomorphism test for graphs with excluded topological subgraphs
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The parameterized complexity of k-edge induced subgraphs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
First-Order and Monadic Second-Order Model-Checking on Ordered Structures
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Deciding first order properties of matroids
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Computing vertex-surjective homomorphisms to partially reflexive trees
Theoretical Computer Science
Constant-factor approximation of the domination number in sparse graphs
European Journal of Combinatorics
Enumerating with constant delay the answers to a query
Proceedings of the 16th International Conference on Database Theory
Enumeration of first-order queries on classes of structures with bounded expansion
Proceedings of the 32nd symposium on Principles of database systems
Testing first-order properties for subclasses of sparse graphs
Journal of the ACM (JACM)
FO model checking of interval graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
A dynamic data structure for counting subgraphs in sparse graphs
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
Distance-two coloring of sparse graphs
European Journal of Combinatorics
Model Checking for Successor-Invariant First-Order Logic on Minor-Closed Graph Classes
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
| Hi-index | 0.00 |
We present a linear-time algorithm for deciding first-order logic (FOL) properties in classes of graphs with bounded expansion. Many natural classes of graphs have bounded expansion: graphs of bounded tree-width, all proper minor-closed classes of graphs, graphs of bounded degree, graphs with no sub graph isomorphic to a subdivision of a fixed graph, and graphs that can be drawn in a fixed surface in such a way that each edge crosses at most a constant number of other edges. We also develop an almost linear-time algorithm for deciding FOL properties in classes of graphs with locally bounded expansion, those include classes of graphs with locally bounded tree-width or locally excluding a minor. More generally, we design a dynamic data structure for graphs belonging to a fixed class of graphs of bounded expansion. After a linear-time initialization the data structure allows us to test an FOL property in constant time, and the data structure can be updated in constant time after addition/deletion of an edge, provided the list of possible edges to be added is known in advance and their addition results in a graph in the class. In addition, we design a dynamic data structure for testing existential properties or the existence of short paths between prescribed vertices in such classes of graphs. All our results also hold for relational structures and are based on the seminal result of Nesetril and Ossona de Mendez on the existence of low tree-depth colorings.