M. Thorup, Compact oracles for reachability and approximate distances in planar digraphs, FOCS 2001, pp. 242-251 Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
An Information-Theoretic Upper Bound of Planar Graphs.. - Bonichon, Gavoille.. (2003) (3 citations) (Correct)
.... [KR99, Ros99] gave a triangulation compressor that guarantees 3:67 bits per node, the best possible rate being log 2 (256=27) 3:24 bits per node from Tutte s enumerative formula [Tut62] Routing table design for a network has been investigated in the case of planar networks [FJ89, GH99, Lu02a, Tho01] The underlying graph of the network is preprocessed in order to optimize routing tables, a data structure dedicated to each node in charge of nding the next output port given the destination address of an incoming message. The main objective is to minimize the size of the routing tables while ....
Mikkel Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In 42 Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE Computer Society Press, October 2001.
An Information Upper Bound of Planar Graphs Using.. - Bonichon, Gavoille.. (2002) (1 citation) (Correct)
.... gave a triangulation compressor that guarantees 3:67 bits per node encoding, the best possible rate being log 2 (256=27) 3:24 bits per node from Tutte s enumerative formula [Tut62] Routing table design for a network has been investigated in the case of planar networks [FJ89, GH99, Lu02a, Tho01] The underlying graph of the network is pre processed in order to optimize routing tables. Such data structures are dedicated to each node in charge of nding the next output port given the destination address of an incoming message. The main objective is to minimize the size of the routing ....
Mikkel Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In 42 Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE Computer Society Press, October 2001.
Compact and Localized Distributed Data Structures - Gavoille, Peleg (2002) (4 citations) (Correct)
....approximate distance labeling scheme on the class of trees. However, distances in a tree between vertices at distance at most d can be computed with labels of log n O(d log n ) bits [71] A similar phenomenon between the label length and the quality of the estimators holds for planar graphs. [118] has presented for planar digraphs a (1 ffl; 0) approximate scheme with O( ffl log n) bit labels, for every ffl 0, to be contrasted with the fact that for ffl = 0 labels must have Omega ) bits [64] Additional results appear in [23,118] A number of additional approximate distance ....
....quality of the estimators holds for planar graphs. 118] has presented for planar digraphs a (1 ffl; 0) approximate scheme with O( ffl log n) bit labels, for every ffl 0, to be contrasted with the fact that for ffl = 0 labels must have Omega ) bits [64] Additional results appear in [23,118]. A number of additional approximate distance labeling schemes are presented in [60] including a (1; 2) approximate scheme with O(log n) bit labels for permutation graphs (namely, graphs constructed from a permutation oe on the vertices such that i and j are adjacent iff i j and oe(i) oe(j) ....
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M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In Proc. 42 IEEE Symp. on Foundations of Computer Science, Oct. 2001.
Reachability and Distance Queries Via 2-Hop Labels - Cohen, Halperin, Kaplan, Zwick (2002) (2 citations) (Correct)
....is important as a less constrained variant often enjoys a more compact labeling. One such example is the family of directed planar graphs: Reachability or (1 #) approximate shortest paths have worst case 2 hop labels of size O(n log n) using some slight modification of a construction by Thorup [11]) whereas for exact distances, there is a known #(n ) lower bound for any labeling scheme [4] It is also not too hard to construct specific graphs which admit more compact labeling for less constrained variants. Thus, 2 hop labels should always be produced for the least constrained appropriate ....
....labeling: Graphs with separator decomposition of size O(n ) have 2 hop labels of size O(n log n) e.g. see [2] It is possible that the optimal 2 hop labeling for small separator graphs is o(n log n) This would be the case if our Conjecture 5.1 is true. For planar graphs, Thorup [11] shows that O(n log n) size reachability and approximate distance labels are possible. It follows from his construction that there are corresponding 2 hop labels of size O(n log n) We are not aware of a matching lower bound for 2 hop reachability labelings, thus, it is possible that there are ....
M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In Proc. 42nd IEEE Annual Symposium on Foundations of Computer Science, 2001.
Optimal Distance Labeling for Interval and Circular-arc Graphs - Gavoille, Paul (Correct)
....upper and lower bounds for these two latter results. The upper bound for planar graphs is O( n log n) coming from a more general result about graphs having small separators. Related works concern distance labeling schemes in dynamic tree networks [22] and approximate distance labeling schemes [12,27,28]. Several ecient schemes have been designed for speci c graph families: interval and permutation graphs [21] distance hereditary graphs [13] bounded tree width graphs (or graphs with bounded vertex separator) and more generally bounded clique width graphs [9] All support an O(log ....
M. Thorup, Compact oracles for reachability and approximate distances in planar digraphs, in 42 IEEE Symp. on Foundations of Computer Science (FOCS), 2001.
Reachability and Distance Queries Via 2-Hop Labels - Cohen, Halperin, Kaplan, Zwick (2002) (2 citations) (Correct)
....important as a less constrained variant often enjoys a more compact labeling. One such example is the family of directed planar graphs: Reachability or (1 ffl) approximate shortest paths have worstcase 2 hop labels of size O(n log n) using some slight modification of a construction by Thorup [11]) whereas for exact distances, there is a known Omega Gamma n ) lower bound for any labeling scheme [4] It is also not too hard to construct specific graphs which admit more compact labeling for less constrained variants. Thus, 2 hop labels should always be produced for the least constrained ....
....compact 2 hop labeling: Graphs with separator decomposition of ) have 2 hop labels of size O(n log n) e.g. see [2] It is possible that the optimal 2 hop labeling for small separator graphs is o(n log n) This would be the case if our Conjecture 5.1 is true. For planar graphs, Thorup [11] shows that O(n log n) size reachability and approximate distance labels are possible. It follows from his construction that there are corresponding 2 hop labels of size O(n log n) We are not aware of a matching lower bound for 2 hop reachability labelings, thus, it is possible that there are ....
M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In Proc. 42nd IEEE Annual Symposium on Foundations of Computer Science, 2001.
Small Universal Distance Matrices - Gavoille, Paul (2003) (Correct)
....bounds for these two latter results. The upper bound for planar graphs is O( n log n) coming from a more general result about graphs having small separators. Related works concern distance labeling schemes in dynamic tree networks [KPR02] and approximate distance labeling schemes [GKK 01, Tho01, TZ01a] Several ecient schemes have been designed for speci c graph families: interval and permutation graphs [KKP00] distance hereditary graphs [GP01a] bounded tree width and more generally bounded clique width graphs [CV01] all support an O(log labeling scheme. Excepted for the two rst ....
M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In 42 Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE Computer Society Press, October 2001.
Approximate Distance Oracles - Thorup, Zwick (2001) (33 citations) Self-citation (Thorup) (Correct)
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M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, Las Vegas, Nevada, pages 242--251, 2001.
Approximate Distance Oracles - Thorup, Zwick (2001) (33 citations) Self-citation (Thorup) (Correct)
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M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs, 2001. Submitted.
Distance and Routing Labeling Schemes for Non-Poositively Curved.. - Chepoi (2003) (Correct)
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M. Thorup, Compact oracles for reachability and approximate distances in planar digraphs, FOCS 2001, pp. 242-251
Exact and Approximate Distances in Graphs - a survey - Zwick (2001) (8 citations) (Correct)
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M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs. manuscript, 2001.
Computing the Shortest Path: A* Search Meets Graph Theory - Goldberg, Harrelson (2004) (Correct)
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M. Thorup. Compact Oracles for Reachability and Approximate Distances in Planar Digraphs. In Proc. 42nd IEEE Annual Symposium on Foundations of Computer Science, pages 242-251, 2001.
Reachability and Distance Queries via 2-Hop Labels - Cohen, Halperin, Kaplan, Zwick (2002) (2 citations) (Correct)
No context found.
M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In Proc. 42nd IEEE Annual Symposium on Foundations of Computer Science, 2001.
Planar Graphs, via Well-Orderly Maps and Trees - Bonichon, Gavoille, Hanusse.. (Correct)
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Mikkel Thorup. Compact oracles for reachability and approximate distances in planar digraphs. Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE Computer Society Press, October 2001.
Improved Compact Routing Scheme for Chordal Graphs - Dourisboure, Gavoille (2002) (3 citations) (Correct)
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Mikkel Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In 42 Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE Computer Society Press, October 2001.
Well-Separated Pair Decomposition for the Unit-Disk Graph.. - Gao, Zhang (2003) (Correct)
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M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In Proc. 42nd IEEE Symposium on Foundations of Computer Science, pages 242--251, 2001.
An Information-Theoretic Upper Bound of Planar Graphs.. - Bonichon, Gavoille.. (2003) (3 citations) (Correct)
No context found.
M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In 42 FOCS. IEEE Computer Society Press, Oct. 2001.
Computing Shortest Paths with Comparisons and Additions - Pettie, Ramachandran (2002) (4 citations) (Correct)
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M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In Proc. FOCS 2001.
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