Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
FAST ALGORITHMS FOR CONSTRUCTING t-SPANNERS AND PATHS WITH STRETCH t. |
| Συγγραφείς: |
Cohen, Edith |
| Πηγή: |
SIAM Journal on Computing; 1998, Vol. 28 Issue 1, p210, 27p |
| Θεματικοί όροι: |
Algorithms, Graphic methods |
| Περίληψη: |
The distance between two vertices in a weighted graph is the weight of a minimum- weight path between them (where the weight of a path is the sum of the weights of the edges in the path). A path has stretch t if its weight is at most t times the distance between its end points. We present algorithms that compute paths of stretch 2 ≤ t ≤ log n on undirected graphs G = (V, E) with nonnegative weights. The stretch t is of the form t = β(2 + ∊), where β is integral and &espi;' > 0 is at least as large as some fixed ∊ > 0. We present an Õ((m + k) n[SUP2 + ∊]/t]) time randomized algorithm that finds paths between k specified pairs of vertices and an n[SUP2(1 + log[SUBn] m + ∊)/t]) deterministic algorithm that finds paths from s specified sources to all other vertices (for any fixed ∊ > 0), where n = |V| and m = |E|. This improves significantly over the slower Õ(min{k,n}m) exact shortest paths algorithms and a previous O(mn&frac64t;] + , kn[SUP&fr4ac32t;]) time algorithm by Awerbuch et al. [Proc. 34th IEEE Annual Symposium on Foundations of Computer Science, IEEE, Piscataway, NJ, 1993, pp. 638-6471. A t-spanner of a graph G is a set of weighted edges on the vertices of G such that distances in the spanner are not smaller and within a factor of t from the corresponding distances in G. Previous work was concerned with bounding the size and efficiently constructing t-spanners. We construct t-spanners of size Õ(n[SUP1+(2 + ∊)]/t) in Õ(mn(2 + ∊)/t) expected time (for any fixed ∊ > 0), which constitutes a faster construction (by a factor of n[SUP3+2/t]/m) of sparser spanners than was previously attainable. We also provide efficient parallel constructions. Our algorithms are based on pairwise covers and a novel approach to construct them efficiently. [ABSTRACT FROM AUTHOR] |
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| Βάση Δεδομένων: |
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