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Approximate distance oracles
The most impressive feature of the data structure is its "constant" query time, hence the name "oracle", which provides faster constructions of sparse spanners of weighted graphs, and improved distance labelings of weighted or unweighted graphs.
Reachability and distance queries via 2-hop labels
- E. Cohen, E. Halperin, Haim Kaplan, U. Zwick
- Computer ScienceACM-SIAM Symposium on Discrete Algorithms
- 6 January 2002
The proposed data structure for representing all distances in a graph is distributed in the sense that it may be viewed as assigning labels to the vertices, such that a query involving vertices u and v may be answered using only the labels of u andV.
The Complexity of Mean Payoff Games on Graphs
A novel randomized method, the method of color-coding for finding simple paths and cycles of a specified length k, and other small subgraphs, within a given graph G = (V,E), which can be derandomized using families of perfect hash functions.
Finding and counting given length cycles
An assortment of methods for finding and counting simple cycles of a given length in directed and undirected graphs improve upon various previously known results.
All pairs shortest paths using bridging sets and rectangular matrix multiplication
- U. Zwick
- Computer ScienceJACM
- 16 August 2000
Two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs using fast matrix multiplication algorithms are presented.
Compact routing schemes
Several compact routing schemes for general weighted undirected networks are described, which achieve a near-optimal tradeoff between the size of the routing tables used and the resulting stretch.
A 7/8-approximation algorithm for MAX 3SAT?
- H. Karloff, U. Zwick
- Computer ScienceProceedings 38th Annual Symposium on Foundations…
- 19 October 1997
A randomized approximation algorithm which takes an instance of MAX 3SAT as input that is optimal if the instance-a collection of clauses each of length at most three-is satisfiable, and a method of obtaining direct semidefinite relaxations of any constraint satisfaction problem of the form MAX CSP(F), where F is a finite family of Boolean functions.
All pairs almost shortest paths
- D. Dor, S. Halperin, U. Zwick
- Computer Science, MathematicsProceedings of 37th Conference on Foundations of…
- 14 October 1996
The algorithm APASP/sub 2/ is simple, easy to implement, and faster than the fastest known matrix multiplication algorithm and it is shown that any weighted undirected graph on n vertices has a 3-spanner with O/spl tilde/(n/sup 3/2/m/sup 1/2/.
Improved Rounding Techniques for the MAX 2-SAT and MAX DI-CUT Problems
Improved approximation algorithms for the MAX 2-SAT and MAX DI-CUT problems are obtained, which are essentially the best performance ratios that can be achieved using any combination of prerounding rotations and skewed distributions of hyperplanes, and even using more general families of rounding procedures.