Spanners of bounded degree graphs
Information Processing Letters
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SIAM Journal on Discrete Mathematics
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Proceedings of the forty-third annual ACM symposium on Theory of computing
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Journal of Computer and System Sciences
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Approximating fault-tolerant group-Steiner problems
Theoretical Computer Science
Power grid analysis with hierarchical support graphs
Proceedings of the International Conference on Computer-Aided Design
The laplacian paradigm: emerging algorithms for massive graphs
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications
Computer Science Review
Integral cycle bases for cyclic timetabling
Discrete Optimization
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ACM Transactions on Algorithms (TALG)
Algorithms, graph theory, and the solution of laplacian linear equations
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Approximation algorithms and hardness results for shortest path based graph orientations
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Parallel graph decompositions using random shifts
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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We show that every weighted connected graph $G$ contains as a subgraph a spanning tree into which the edges of $G$ can be embedded with average stretch $O (\log^{2} n \log \log n)$. Moreover, we show that this tree can be constructed in time $O (m \log n + n \log^2 n)$ in general, and in time $O (m \log n)$ if the input graph is unweighted. The main ingredient in our construction is a novel graph decomposition technique. Our new algorithm can be immediately used to improve the running time of the recent solver for symmetric diagonally dominant linear systems of Spielman and Teng from $ m 2^{(O (\sqrt{\log n\log\log n})) }$ to $m \log^{O (1)}n$, and to $O ( n \log^{2} n \log \log n)$ when the system is planar. Our result can also be used to improve several earlier approximation algorithms that use low-stretch spanning trees.