Arboricity and subgraph listing algorithms
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Fixed-Parameter Tractability and Completeness I: Basic Results
SIAM Journal on Computing
On efficient fixed-parameter algorithms for weighted vertex cover
Journal of Algorithms
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Studying (non-planar) road networks through an algorithmic lens
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
The h-Index of a Graph and Its Application to Dynamic Subgraph Statistics
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
A dynamic data structure for counting subgraphs in sparse graphs
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We present techniques for maintaining subgraph frequencies in a dynamic graph, using data structures that are parameterized in terms of h, the h- index of the graph. Our methods extend previous results of Eppstein and Spiro for maintaining statistics for undirected subgraphs of size three to directed subgraphs and to subgraphs of size four. For the directed case, we provide a data structure to maintain counts for all 3-vertex induced subgraphs in O(h) amortized time per update. For the undirected case, we maintain the counts of size-four subgraphs in O(h2) amortized time per update. These extensions enable a number of new applications in Bioinformatics and Social Networking research.