Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
Near-Linear Time Construction of Sparse Neighborhood Covers
SIAM Journal on Computing
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Journal of Algorithms
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Introduction to Algorithms
Approximate distance oracles for unweighted graphs in Õ (n2) time
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
Journal of the ACM (JACM)
A simple linear time algorithm for computing a (2k - 1)-spanner of o(n1+1/k) size in weighted graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximate distance oracles for unweighted graphs in expected O(n2) time
ACM Transactions on Algorithms (TALG)
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
Dynamic algorithms for graph spanners
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Bounded-leg distance and reachability oracles
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Fully dynamic algorithm for graph spanners with poly-logarithmic update time
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Compact name-independent routing with minimum stretch
ACM Transactions on Algorithms (TALG)
Fast deterministic distributed algorithms for sparse spanners
Theoretical Computer Science
Distributed algorithms for ultrasparse spanners and linear size skeletons
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
All-pairs nearly 2-approximate shortest paths in O(n2polylogn) time
Theoretical Computer Science
Approximating Shortest Paths in Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Fault-tolerant spanners for general graphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Small stretch (α,β)-spanners in the streaming model
Theoretical Computer Science
ACM Transactions on Algorithms (TALG)
As Good as It Gets: Competitive Fault Tolerance in Network Structures
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Small stretch spanners in the streaming model: new algorithms and experiments
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Local computation of nearly additive spanners
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Additive spanners in nearly quadratic time
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Computing graph spanners in small memory: fault-tolerance and streaming
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
f-sensitivity distance Oracles and routing schemes
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Approximation of minimum weight spanners for sparse graphs
Theoretical Computer Science
Faster Algorithms for All-pairs Approximate Shortest Paths in Undirected Graphs
SIAM Journal on Computing
Fault Tolerant Spanners for General Graphs
SIAM Journal on Computing
Distance oracles for vertex-labeled graphs
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Approximate distance oracles with improved preprocessing time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fast deterministic distributed algorithms for sparse spanners
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
On spanners of geometric graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Small stretch spanners on dynamic graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Fast, precise and dynamic distance queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Fully dynamic randomized algorithms for graph spanners
ACM Transactions on Algorithms (TALG)
Deterministic distributed construction of linear stretch spanners in polylogarithmic time
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Improved distance oracles and spanners for vertex-labeled graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Fault tolerant additive spanners
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Efficient distributed source detection with limited bandwidth
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Small stretch pairwise spanners
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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Thorup and Zwick showed that for any integer k≥ 1, it is possible to preprocess any positively weighted undirected graph G=(V,E), with |E|=m and |V|=n, in Õ(kmn$^{\rm 1/{\it k}}$) expected time and construct a data structure (a (2k–1)-approximate distance oracle) of size O(kn$^{\rm 1+1/{\it k}}$) capable of returning in O(k) time an approximation $\hat{\delta}(u,v)$ of the distance δ(u,v) from u to v in G that satisfies $\delta(u,v) \leq \hat{\delta}(u,v) \leq (2k -1)\cdot \delta(u,v)$, for any two vertices u,v∈ V. They also presented a much slower Õ(kmn) time deterministic algorithm for constructing approximate distance oracle with the slightly larger size of O(kn$^{\rm 1+1/{\it k}}$log n). We present here a deterministic Õ(kmn$^{\rm 1/{\it k}}$) time algorithm for constructing oracles of size O(kn$^{\rm 1+1/{\it k}}$). Our deterministic algorithm is slower than the randomized one by only a logarithmic factor. Using our derandomization technique we also obtain the first deterministic linear time algorithm for constructing optimal spanners of weighted graphs. We do that by derandomizing the O(km) expected time algorithm of Baswana and Sen (ICALP’03) for constructing (2k–1)-spanners of size O(kn$^{\rm 1+1/{\it k}}$) of weighted undirected graphs without incurring any asymptotic loss in the running time or in the size of the spanners produced.