Streaming algorithms for independent sets
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
ACM Transactions on Algorithms (TALG)
A tight unconditional lower bound on distributed randomwalk computation
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Improved approximation for the directed spanner problem
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Linear programming in the semi-streaming model with application to the maximum matching problem
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Everywhere-tight information cost tradeoffs for augmented index
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Analyzing graph structure via linear measurements
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Of hammers and nails: an empirical comparison of three paradigms for processing large graphs
Proceedings of the fifth ACM international conference on Web search and data mining
Graph sketches: sparsification, spanners, and subgraphs
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Fully dynamic randomized algorithms for graph spanners
ACM Transactions on Algorithms (TALG)
Label cover instances with large girth and the hardness of approximating basic k-spanner
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Space-constrained interval selection
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Streaming and communication complexity of clique approximation
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Linear programming in the semi-streaming model with application to the maximum matching problem
Information and Computation
Approximation algorithms for spanner problems and Directed Steiner Forest
Information and Computation
A modelling framework for social media monitoring
International Journal of Web Engineering and Technology
Mining most frequently changing component in evolving graphs
World Wide Web
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We explore problems related to computing graph distances in the data-stream model. The goal is to design algorithms that can process the edges of a graph in an arbitrary order given only a limited amount of working memory. We are motivated by both the practical challenge of processing massive graphs such as the web graph and the desire for a better theoretical understanding of the data-stream model. In particular, we are interested in the trade-offs between model parameters such as per-data-item processing time, total space, and the number of passes that may be taken over the stream. These trade-offs are more apparent when considering graph problems than they were in previous streaming work that solved problems of a statistical nature. Our results include the following: (1) Spanner construction: There exists a single-pass, $\tilde{O}(tn^{1+1/t})$-space, $\tilde{O}(t^2n^{1/t})$-time-per-edge algorithm that constructs a $(2t+1)$-spanner. For $t=\Omega(\log n/{\log\log n})$, the algorithm satisfies the semistreaming space restriction of $O(n\operatorname{polylog}n)$ and has per-edge processing time $O(\operatorname{polylog}n)$. This resolves an open question from [J. Feigenbaum et al., Theoret. Comput. Sci., 348 (2005), pp. 207-216]. (2) Breadth-first-search (BFS) trees: For any even constant $k$, we show that any algorithm that computes the first $k$ layers of a BFS tree from a prescribed node with probability at least $2/3$ requires either greater than $k/2$ passes or $\tilde{\Omega}(n^{1+1/k})$ space. Since constructing BFS trees is an important subroutine in many traditional graph algorithms, this demonstrates the need for new algorithmic techniques when processing graphs in the data-stream model. (3) Graph-distance lower bounds: Any $t$-approximation of the distance between two nodes requires $\Omega(n^{1+1/t})$ space. We also prove lower bounds for determining the length of the shortest cycle and other graph properties. (4) Techniques for decreasing per-edge processing: We discuss two general techniques for speeding up the per-edge computation time of streaming algorithms while increasing the space by only a small factor.