Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs
Let G be a graph where each vertex is associated with a label. A vertex-labeled approximate distance oracle is a data structure that, given a vertex v and a label λ , returns a (1 + ε )-approximation of the distance from v to the closest vertex with label λ in G . Such an oracle is dynamic if it als...
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| Vydáno v: | Theory of computing systems Ročník 63; číslo 8; s. 1849 - 1874 |
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01.11.2019
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| ISSN: | 1432-4350, 1433-0490 |
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| Abstract | Let
G
be a graph where each vertex is associated with a label. A
vertex-labeled approximate distance oracle
is a data structure that, given a vertex
v
and a label
λ
, returns a (1 +
ε
)-approximation of the distance from
v
to the closest vertex with label
λ
in
G
. Such an oracle is
dynamic
if it also supports label changes. In this paper we present three different dynamic approximate vertex-labeled distance oracles for planar graphs, all with polylogarithmic query and update times, and nearly linear space requirements. No such oracles were previously known. |
|---|---|
| AbstractList | Let G be a graph where each vertex is associated with a label. A vertex-labeled approximate distance oracle is a data structure that, given a vertex v and a label λ, returns a (1 + ε)-approximation of the distance from v to the closest vertex with label λ in G. Such an oracle is dynamic if it also supports label changes. In this paper we present three different dynamic approximate vertex-labeled distance oracles for planar graphs, all with polylogarithmic query and update times, and nearly linear space requirements. No such oracles were previously known. Let G be a graph where each vertex is associated with a label. A vertex-labeled approximate distance oracle is a data structure that, given a vertex v and a label λ , returns a (1 + ε )-approximation of the distance from v to the closest vertex with label λ in G . Such an oracle is dynamic if it also supports label changes. In this paper we present three different dynamic approximate vertex-labeled distance oracles for planar graphs, all with polylogarithmic query and update times, and nearly linear space requirements. No such oracles were previously known. |
| Author | Laish, Itay Mozes, Shay |
| Author_xml | – sequence: 1 givenname: Itay surname: Laish fullname: Laish, Itay organization: Efi Arazi School of Computer Science, The Interdisciplinary Center Herzliya – sequence: 2 givenname: Shay orcidid: 0000-0001-9262-1821 surname: Mozes fullname: Mozes, Shay email: smozes@idc.ac.il organization: Efi Arazi School of Computer Science, The Interdisciplinary Center Herzliya |
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| Cites_doi | 10.1007/978-3-642-38236-9_5 10.1145/2530531 10.1137/1.9781611974331.ch26 10.1006/jcss.1997.1493 10.1007/978-3-662-48971-0_53 10.1145/1039488.1039493 10.1145/380752.380798 10.1007/978-3-642-22012-8_39 10.1007/s00224-017-9827-0 10.1007/978-3-642-22006-7_12 10.1137/1.9781611973099.18 10.1145/2213977.2214084 10.1007/978-3-642-33090-2_29 10.1145/828.1884 10.1137/0136016 10.1145/2746539.2746615 10.1007/978-3-319-28684-6_9 10.1007/978-3-662-44777-2_69 10.1007/3-540-44676-1_10 10.1016/0020-0190(83)90075-3 10.1137/1.9781611973105.40 10.1137/1.9781611974331.ch53 |
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| Keywords | cover Approximate distance oracles Vertex labels Portals Planar graphs |
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| References | Hermelin, D., Levy, A., Weimann, O., Yuster, R.: Distance oracles for vertex-labeled graphs. In: ICALP (2), Lecture Notes in Computer Science, vol. 6756, pp. 490–501. Springer (2011) Li, M., Ma, C.C.C.: Ning, L.: (1 + 𝜖)-distance oracles for vertex-labeled planar graphs. In: TAMC, pp. 42–51 (2013) SommerCShortest-path queries in static networksACM Comput. Surv.201446445:145:3110.1145/25305311305.68137 WilkinsonBryan T.Amortized Bounds for Dynamic Orthogonal Range ReportingAlgorithms - ESA 20142014Berlin, HeidelbergSpringer Berlin Heidelberg84285610.1007/978-3-662-44777-2_69 MozesShaySkopEyal E.Efficient Vertex-Label Distance Oracles for Planar GraphsTheory of Computing Systems2017622419440376771910.1007/s00224-017-9827-0 Klein, P.N.: Multiple-source shortest paths in planar graphs. In: SODA, pp. 146–155 (2005) Chechik, S.: Improved distance oracles and spanners for vertex-labeled graphs. In: ESA, Lecture Notes in Computer Science, vol. 7501, pp. 325–336. Springer (2012) Klein, P.N.: Preprocessing an undirected planar network to enable fast approximate distance queries. In: SODA, pp. 820–827 (2002) ThorupMCompact oracles for reachability and approximate distances in planar digraphsJ. ACM20045169931024214526110.1145/1039488.10394931125.68394 Wulff-Nilsen, C.: Approximate distance oracles with improved preprocessing time. In: SODA, pp. 202–208. SIAM (2012) HenzingerMRKleinPNRaoSSubramanianSFaster shortest-path algorithms for planar graphsJ. Comput. Syst. Sci.1997551323147304610.1006/jcss.1997.14930880.68099 Thorup, M., Zwick, U.: Approximate distance oracles. In: STOC, pp. 183–192. ACM (2001) Wulff-Nilsen, C.: Approximate distance oracles for planar graphs with improved query time-space tradeoff. In: SODA, pp. 351–362 (2016) Łȧcki, J., Ocwieja, J., Pilipczuk, M., Sankowski, P., Zych, A.: The power of dynamic distance oracles: efficient dynamic algorithms for the steiner tree. In: STOC, pp. 11–20 (2015) PaghRasmusRodlerFlemming FricheCuckoo HashingAlgorithms — ESA 20012001Berlin, HeidelbergSpringer Berlin Heidelberg12113310.1007/3-540-44676-1_10 Kawarabayashi, K., Klein, P.N., Sommer, C.: Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs. In: ICALP (1), Lecture Notes in Computer Science, vol. 6755, pp. 135–146. Springer (2011) WillardDELog-logarithmic worst-case range queries are possible in space theta(n)Inf. Process. Lett.1983172818410.1016/0020-0190(83)90075-30509.68106 Abraham, I., Chechik, S., Gavoille, C.: Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels. In: STOC, pp. 1199–1218. ACM (2012) Abraham, I., Chechik, S., Delling, D., Goldberg, A.V., Werneck, R.F.: On dynamic approximate shortest paths for planar graphs with worst-case costs. In: SODA, pp. 740–753. SIAM (2016) LiptonRJTarjanREA separator theorem for planar graphsSIAM J. Appl. Math.197936217718952449510.1137/0136016 Kawarabayashi, K., Sommer, C., Thorup, M.: More compact oracles for approximate distances in undirected planar graphs. In: SODA, pp. 550–563. SIAM (2013) Gu, Q., Xu, G.: Constant query time (1 + 𝜖)-approximate distance oracle for planar graphs. In: ISAAC, pp. 625–636 (2015) MozesShaySkopEyal E.Efficient Vertex-Label Distance Oracles for Planar GraphsApproximation and Online Algorithms2015ChamSpringer International Publishing9710910.1007/978-3-319-28684-6_9 FredmanMLKomlȯsJSzemerėdiEStoring a sparse table with O(1) worst case access timeJ. ACM,198431353854481915610.1145/828.18840629.68068 M Thorup (9949_CR19) 2004; 51 9949_CR9 RJ Lipton (9949_CR13) 1979; 36 Bryan T. Wilkinson (9949_CR21) 2014 9949_CR20 MR Henzinger (9949_CR6) 1997; 55 Rasmus Pagh (9949_CR17) 2001 DE Willard (9949_CR22) 1983; 17 9949_CR12 9949_CR23 9949_CR24 9949_CR10 Shay Mozes (9949_CR15) 2015 ML Fredman (9949_CR4) 1984; 31 9949_CR11 9949_CR14 Shay Mozes (9949_CR16) 2017; 62 9949_CR2 C Sommer (9949_CR18) 2014; 46 9949_CR1 9949_CR3 9949_CR5 9949_CR8 9949_CR7 |
| References_xml | – reference: Gu, Q., Xu, G.: Constant query time (1 + 𝜖)-approximate distance oracle for planar graphs. In: ISAAC, pp. 625–636 (2015) – reference: Łȧcki, J., Ocwieja, J., Pilipczuk, M., Sankowski, P., Zych, A.: The power of dynamic distance oracles: efficient dynamic algorithms for the steiner tree. In: STOC, pp. 11–20 (2015) – reference: ThorupMCompact oracles for reachability and approximate distances in planar digraphsJ. ACM20045169931024214526110.1145/1039488.10394931125.68394 – reference: Thorup, M., Zwick, U.: Approximate distance oracles. In: STOC, pp. 183–192. ACM (2001) – reference: WilkinsonBryan T.Amortized Bounds for Dynamic Orthogonal Range ReportingAlgorithms - ESA 20142014Berlin, HeidelbergSpringer Berlin Heidelberg84285610.1007/978-3-662-44777-2_69 – reference: Kawarabayashi, K., Klein, P.N., Sommer, C.: Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs. In: ICALP (1), Lecture Notes in Computer Science, vol. 6755, pp. 135–146. Springer (2011) – reference: Li, M., Ma, C.C.C.: Ning, L.: (1 + 𝜖)-distance oracles for vertex-labeled planar graphs. In: TAMC, pp. 42–51 (2013) – reference: Abraham, I., Chechik, S., Gavoille, C.: Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels. In: STOC, pp. 1199–1218. ACM (2012) – reference: PaghRasmusRodlerFlemming FricheCuckoo HashingAlgorithms — ESA 20012001Berlin, HeidelbergSpringer Berlin Heidelberg12113310.1007/3-540-44676-1_10 – reference: Abraham, I., Chechik, S., Delling, D., Goldberg, A.V., Werneck, R.F.: On dynamic approximate shortest paths for planar graphs with worst-case costs. In: SODA, pp. 740–753. SIAM (2016) – reference: WillardDELog-logarithmic worst-case range queries are possible in space theta(n)Inf. Process. Lett.1983172818410.1016/0020-0190(83)90075-30509.68106 – reference: Klein, P.N.: Multiple-source shortest paths in planar graphs. In: SODA, pp. 146–155 (2005) – reference: HenzingerMRKleinPNRaoSSubramanianSFaster shortest-path algorithms for planar graphsJ. Comput. Syst. Sci.1997551323147304610.1006/jcss.1997.14930880.68099 – reference: MozesShaySkopEyal E.Efficient Vertex-Label Distance Oracles for Planar GraphsApproximation and Online Algorithms2015ChamSpringer International Publishing9710910.1007/978-3-319-28684-6_9 – reference: LiptonRJTarjanREA separator theorem for planar graphsSIAM J. Appl. Math.197936217718952449510.1137/0136016 – reference: Wulff-Nilsen, C.: Approximate distance oracles for planar graphs with improved query time-space tradeoff. In: SODA, pp. 351–362 (2016) – reference: Hermelin, D., Levy, A., Weimann, O., Yuster, R.: Distance oracles for vertex-labeled graphs. In: ICALP (2), Lecture Notes in Computer Science, vol. 6756, pp. 490–501. Springer (2011) – reference: Kawarabayashi, K., Sommer, C., Thorup, M.: More compact oracles for approximate distances in undirected planar graphs. In: SODA, pp. 550–563. SIAM (2013) – reference: Wulff-Nilsen, C.: Approximate distance oracles with improved preprocessing time. In: SODA, pp. 202–208. SIAM (2012) – reference: Klein, P.N.: Preprocessing an undirected planar network to enable fast approximate distance queries. In: SODA, pp. 820–827 (2002) – reference: FredmanMLKomlȯsJSzemerėdiEStoring a sparse table with O(1) worst case access timeJ. ACM,198431353854481915610.1145/828.18840629.68068 – reference: SommerCShortest-path queries in static networksACM Comput. Surv.201446445:145:3110.1145/25305311305.68137 – reference: Chechik, S.: Improved distance oracles and spanners for vertex-labeled graphs. In: ESA, Lecture Notes in Computer Science, vol. 7501, pp. 325–336. Springer (2012) – reference: MozesShaySkopEyal E.Efficient Vertex-Label Distance Oracles for Planar GraphsTheory of Computing Systems2017622419440376771910.1007/s00224-017-9827-0 – ident: 9949_CR10 – ident: 9949_CR12 doi: 10.1007/978-3-642-38236-9_5 – volume: 46 start-page: 45:1 issue: 4 year: 2014 ident: 9949_CR18 publication-title: ACM Comput. Surv. doi: 10.1145/2530531 – ident: 9949_CR24 doi: 10.1137/1.9781611974331.ch26 – volume: 55 start-page: 3 issue: 1 year: 1997 ident: 9949_CR6 publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.1997.1493 – ident: 9949_CR11 – ident: 9949_CR5 doi: 10.1007/978-3-662-48971-0_53 – volume: 51 start-page: 993 issue: 6 year: 2004 ident: 9949_CR19 publication-title: J. ACM doi: 10.1145/1039488.1039493 – ident: 9949_CR20 doi: 10.1145/380752.380798 – ident: 9949_CR7 doi: 10.1007/978-3-642-22012-8_39 – volume: 62 start-page: 419 issue: 2 year: 2017 ident: 9949_CR16 publication-title: Theory of Computing Systems doi: 10.1007/s00224-017-9827-0 – ident: 9949_CR8 doi: 10.1007/978-3-642-22006-7_12 – ident: 9949_CR23 doi: 10.1137/1.9781611973099.18 – ident: 9949_CR2 doi: 10.1145/2213977.2214084 – ident: 9949_CR3 doi: 10.1007/978-3-642-33090-2_29 – volume: 31 start-page: 538 issue: 3 year: 1984 ident: 9949_CR4 publication-title: J. ACM, doi: 10.1145/828.1884 – volume: 36 start-page: 177 issue: 2 year: 1979 ident: 9949_CR13 publication-title: SIAM J. Appl. Math. doi: 10.1137/0136016 – ident: 9949_CR14 doi: 10.1145/2746539.2746615 – start-page: 97 volume-title: Approximation and Online Algorithms year: 2015 ident: 9949_CR15 doi: 10.1007/978-3-319-28684-6_9 – start-page: 842 volume-title: Algorithms - ESA 2014 year: 2014 ident: 9949_CR21 doi: 10.1007/978-3-662-44777-2_69 – start-page: 121 volume-title: Algorithms — ESA 2001 year: 2001 ident: 9949_CR17 doi: 10.1007/3-540-44676-1_10 – volume: 17 start-page: 81 issue: 2 year: 1983 ident: 9949_CR22 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(83)90075-3 – ident: 9949_CR9 doi: 10.1137/1.9781611973105.40 – ident: 9949_CR1 doi: 10.1137/1.9781611974331.ch53 |
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| Snippet | Let
G
be a graph where each vertex is associated with a label. A
vertex-labeled approximate distance oracle
is a data structure that, given a vertex
v
and a... Let G be a graph where each vertex is associated with a label. A vertex-labeled approximate distance oracle is a data structure that, given a vertex v and a... |
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| SubjectTerms | Computer Science Data structures Graphs Special Issue on Approximation and Online Algorithms Theory of Computation |
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| Title | Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs |
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| Volume | 63 |
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