Polylogarithmic-overhead piecemeal graph exploration

Baruch Awerbuch, Stephen G Kobourov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

Abstract

We introduce a new traversal technique in the context of piecemeal exploration of unknown graphs. The problem of learning a graph via piecemeal exploration requires a robot to create a complete map of its environment, subject to two constraints. First, it cannot jump between non-adjacent vertices in one time step and second, it must return to a fixed starting point every so often. This paper presents the recursive piecemeal search (RPS) strategy together with an algorithm for the above problem. We are able to achieve O(log2 n) overhead (where n is the number of vertices), improving on previous results of Awerbuch, Betke, Rivest, and Singh which require O(nε) overhead. The graph is discovered via the recursive piecemeal search, which can be viewed as a combination of breadth-first and depth-first passes. The construction of RPS trees relies on the concept of sparse neighborhood covers and captures nicely the nature of the graph exploration problem.

Original languageEnglish (US)
Title of host publicationProceedings of the Annual ACM Conference on Computational Learning Theory
PublisherACM
Pages280-286
Number of pages7
StatePublished - 1998
Externally publishedYes
EventProceedings of the 1998 11th Annual Conference on Computational Learning Theory - Madison, WI, USA
Duration: Jul 24 1998Jul 26 1998

Other

OtherProceedings of the 1998 11th Annual Conference on Computational Learning Theory
CityMadison, WI, USA
Period7/24/987/26/98

Fingerprint

Robots
Graph in graph theory
Recursive Trees
Breadth
Search Trees
Search Strategy
Jump
Robot
Fixed point
Cover
Unknown
Context
Concepts
Learning

ASJC Scopus subject areas

  • Computational Mathematics

Cite this

Awerbuch, B., & Kobourov, S. G. (1998). Polylogarithmic-overhead piecemeal graph exploration. In Proceedings of the Annual ACM Conference on Computational Learning Theory (pp. 280-286). ACM.

Polylogarithmic-overhead piecemeal graph exploration. / Awerbuch, Baruch; Kobourov, Stephen G.

Proceedings of the Annual ACM Conference on Computational Learning Theory. ACM, 1998. p. 280-286.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Awerbuch, B & Kobourov, SG 1998, Polylogarithmic-overhead piecemeal graph exploration. in Proceedings of the Annual ACM Conference on Computational Learning Theory. ACM, pp. 280-286, Proceedings of the 1998 11th Annual Conference on Computational Learning Theory, Madison, WI, USA, 7/24/98.
Awerbuch B, Kobourov SG. Polylogarithmic-overhead piecemeal graph exploration. In Proceedings of the Annual ACM Conference on Computational Learning Theory. ACM. 1998. p. 280-286
Awerbuch, Baruch ; Kobourov, Stephen G. / Polylogarithmic-overhead piecemeal graph exploration. Proceedings of the Annual ACM Conference on Computational Learning Theory. ACM, 1998. pp. 280-286
@inproceedings{8eea16ab8f904262bf537655a8c6ce6b,
title = "Polylogarithmic-overhead piecemeal graph exploration",
abstract = "We introduce a new traversal technique in the context of piecemeal exploration of unknown graphs. The problem of learning a graph via piecemeal exploration requires a robot to create a complete map of its environment, subject to two constraints. First, it cannot jump between non-adjacent vertices in one time step and second, it must return to a fixed starting point every so often. This paper presents the recursive piecemeal search (RPS) strategy together with an algorithm for the above problem. We are able to achieve O(log2 n) overhead (where n is the number of vertices), improving on previous results of Awerbuch, Betke, Rivest, and Singh which require O(nε) overhead. The graph is discovered via the recursive piecemeal search, which can be viewed as a combination of breadth-first and depth-first passes. The construction of RPS trees relies on the concept of sparse neighborhood covers and captures nicely the nature of the graph exploration problem.",
author = "Baruch Awerbuch and Kobourov, {Stephen G}",
year = "1998",
language = "English (US)",
pages = "280--286",
booktitle = "Proceedings of the Annual ACM Conference on Computational Learning Theory",
publisher = "ACM",

}

TY - GEN

T1 - Polylogarithmic-overhead piecemeal graph exploration

AU - Awerbuch, Baruch

AU - Kobourov, Stephen G

PY - 1998

Y1 - 1998

N2 - We introduce a new traversal technique in the context of piecemeal exploration of unknown graphs. The problem of learning a graph via piecemeal exploration requires a robot to create a complete map of its environment, subject to two constraints. First, it cannot jump between non-adjacent vertices in one time step and second, it must return to a fixed starting point every so often. This paper presents the recursive piecemeal search (RPS) strategy together with an algorithm for the above problem. We are able to achieve O(log2 n) overhead (where n is the number of vertices), improving on previous results of Awerbuch, Betke, Rivest, and Singh which require O(nε) overhead. The graph is discovered via the recursive piecemeal search, which can be viewed as a combination of breadth-first and depth-first passes. The construction of RPS trees relies on the concept of sparse neighborhood covers and captures nicely the nature of the graph exploration problem.

AB - We introduce a new traversal technique in the context of piecemeal exploration of unknown graphs. The problem of learning a graph via piecemeal exploration requires a robot to create a complete map of its environment, subject to two constraints. First, it cannot jump between non-adjacent vertices in one time step and second, it must return to a fixed starting point every so often. This paper presents the recursive piecemeal search (RPS) strategy together with an algorithm for the above problem. We are able to achieve O(log2 n) overhead (where n is the number of vertices), improving on previous results of Awerbuch, Betke, Rivest, and Singh which require O(nε) overhead. The graph is discovered via the recursive piecemeal search, which can be viewed as a combination of breadth-first and depth-first passes. The construction of RPS trees relies on the concept of sparse neighborhood covers and captures nicely the nature of the graph exploration problem.

UR - http://www.scopus.com/inward/record.url?scp=0031633463&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031633463&partnerID=8YFLogxK

M3 - Conference contribution

SP - 280

EP - 286

BT - Proceedings of the Annual ACM Conference on Computational Learning Theory

PB - ACM

ER -