# GENERAL SPANNING TREES AND CORE LABELING

### Yangjun Chen

#### Abstract

The checking of graph reachability is an important opera¬tion in many applications, by which for two given nodes u and v in a directed graph G we will check whether u is reachable from v through a path in G or vice versa. In this paper, we focus ourselves on this issue. A new approach is proposed to compress transitive closure to support reach¬ability. The main idea is the concept of general spanning trees, as well as a new labeling technique, called core labeling. For a graph G with n nodes and e edges, the labeling time is bounded by O(n + e + tb), where t is the number of non-tree edges (edges that do not appear in the general spanning tree T 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. The space and time com¬plexities are bounded by O(n + tb) and O(logb), respectively.

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#### Paper Citation

#### in Harvard Style

Chen Y. (2009). **GENERAL SPANNING TREES AND CORE LABELING** . In *Proceedings of the 4th International Conference on Software and Data Technologies - Volume 1: ICSOFT,* ISBN 978-989-674-009-2, pages 93-98. DOI: 10.5220/0002238500930098

#### in Bibtex Style

@conference{icsoft09,

author={Yangjun Chen},

title={GENERAL SPANNING TREES AND CORE LABELING},

booktitle={Proceedings of the 4th International Conference on Software and Data Technologies - Volume 1: ICSOFT,},

year={2009},

pages={93-98},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002238500930098},

isbn={978-989-674-009-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 4th International Conference on Software and Data Technologies - Volume 1: ICSOFT,

TI - GENERAL SPANNING TREES AND CORE LABELING

SN - 978-989-674-009-2

AU - Chen Y.

PY - 2009

SP - 93

EP - 98

DO - 10.5220/0002238500930098