research-article

General spanning trees and reachability query evaluation

Author:

Yangjun ChenAuthors Info & Claims

C3S2E '09: Proceedings of the 2nd Canadian Conference on Computer Science and Software Engineering

Pages 243 - 252

https://doi.org/10.1145/1557626.1557665

Published: 19 May 2009 Publication History

Abstract

Graph reachability is fundamental to a wide range of applications, including CAD/CAM, CASE, office systems, software management, as well as geographical navigation and internet routing. Many applications involve huge graphs and requires fast answering of reachability queries. Several reachability labeling methods have been proposed for this purpose. They assign labels to the nodes, such that the reachability between any two nodes can be determined using their labels only. In this paper, we propose a new data structure, called a general spanning tree of a directed acyclic graph (DAG) to minimize label space. Different from a traditional spanning tree, an edge in a general spanning tree T of a DAG G may corresponds to a path in G. That is, for each edge u → v in T, we have a path from u to v in G. An algorithm is discussed to find such a tree with the least number of leaf nodes in O(bn √b) time, where n is the number of the nodes of G, and b is the number of the leaf nodes of T. It can be proven that b equals G's width, defined to be the size of a largest node subset U of G such that for every pair of nodes u, v ∈ U, there does not exist a path from u to v or from v to u. Based on T, we are able to reduce the label space to O(bn) with O(logb) reachability query time. Our method can also be extended for graphs containing cycles.

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Cited By

Song YGe XYu JHao RYang M(2024)Enabling Privacy-Preserving K-Hop Reachability Query Over Encrypted GraphsIEEE Transactions on Services Computing10.1109/TSC.2024.338295417:3(893-904)Online publication date: May-2024
https://doi.org/10.1109/TSC.2024.3382954
He DYuan PJin H(2023)Answering reachability queries with ordered label constraints over labeled graphsFrontiers of Computer Science10.1007/s11704-022-2368-y18:1Online publication date: 12-Aug-2023
https://doi.org/10.1007/s11704-022-2368-y
Yuan PYou YZhou SJin HLiu L(2022)Providing Fast Reachability Query Services With MGTag: A Multi-Dimensional Graph Labeling MethodIEEE Transactions on Services Computing10.1109/TSC.2020.296989815:2(1000-1011)Online publication date: 1-Mar-2022
https://doi.org/10.1109/TSC.2020.2969898
Show More Cited By

Index Terms

General spanning trees and reachability query evaluation
1. Information systems
  1. Information retrieval
    1. Information retrieval query processing
2. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Trees

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cover image ACM Other conferences

C3S2E '09: Proceedings of the 2nd Canadian Conference on Computer Science and Software Engineering

May 2009

266 pages

ISBN:9781605584010

DOI:10.1145/1557626

Editors:
Bipin C. Desai
Concordia University
,
Carson K. Leung
University of Manitoba

Copyright © 2009 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 19 May 2009

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C3S2E '09

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Concordia University

C3S2E '09: Proceedings of the 2009 C3S2E conference

May 19 - 21, 2009

Quebec, Montreal, Canada

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Cited By

Song YGe XYu JHao RYang M(2024)Enabling Privacy-Preserving K-Hop Reachability Query Over Encrypted GraphsIEEE Transactions on Services Computing10.1109/TSC.2024.338295417:3(893-904)Online publication date: May-2024
https://doi.org/10.1109/TSC.2024.3382954
He DYuan PJin H(2023)Answering reachability queries with ordered label constraints over labeled graphsFrontiers of Computer Science10.1007/s11704-022-2368-y18:1Online publication date: 12-Aug-2023
https://doi.org/10.1007/s11704-022-2368-y
Yuan PYou YZhou SJin HLiu L(2022)Providing Fast Reachability Query Services With MGTag: A Multi-Dimensional Graph Labeling MethodIEEE Transactions on Services Computing10.1109/TSC.2020.296989815:2(1000-1011)Online publication date: 1-Mar-2022
https://doi.org/10.1109/TSC.2020.2969898
Chen YChen YZhang Y(2022)Evaluation of Reachability Queries Based on Recursive DAG DecompositionIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2022.3220191(1-18)Online publication date: 2022
https://doi.org/10.1109/TKDE.2022.3220191
Treur J(2019)Mathematical analysis of the emergence of communities based on coevolution of social contagion and bonding by homophilyApplied Network Science10.1007/s41109-019-0130-74:1Online publication date: 25-Jun-2019
https://doi.org/10.1007/s41109-019-0130-7
Treur JTreur J(2019)Ins and Outs of Network-Oriented ModelingNetwork-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models10.1007/978-3-030-31445-3_2(25-55)Online publication date: 2-Nov-2019
https://doi.org/10.1007/978-3-030-31445-3_2
Treur JTreur J(2019)Analysis of a Network’s Emerging Behaviour via Its Structure Involving Its Strongly Connected ComponentsNetwork-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models10.1007/978-3-030-31445-3_12(281-318)Online publication date: 2-Nov-2019
https://doi.org/10.1007/978-3-030-31445-3_12
Treur J(2018)The Ins and Outs of Network-Oriented Modeling: From Biological Networks and Mental Networks to Social Networks and BeyondTransactions on Computational Collective Intelligence XXXII10.1007/978-3-662-58611-2_2(120-139)Online publication date: 19-Dec-2018
https://doi.org/10.1007/978-3-662-58611-2_2
Treur J(2018)Mathematical Analysis of a Network’s Asymptotic Behaviour Based on Its Strongly Connected ComponentsComplex Networks and Their Applications VII10.1007/978-3-030-05411-3_53(663-679)Online publication date: 2-Dec-2018
https://doi.org/10.1007/978-3-030-05411-3_53
Xue PNie TShen DKou YLi W(2014)A Reachability Query Approach with Path Interval LabelingProceedings of the 2014 11th Web Information System and Application Conference10.1109/WISA.2014.39(172-177)Online publication date: 12-Sep-2014
https://dl.acm.org/doi/10.1109/WISA.2014.39
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