A simple way to improve path consistency processing in interval algebra networks
Abstract
Reasoning about qualitative temporal information is essential in many artificial intelligence problems. In particular, many tasks can be solved using the intervalbased temporal algebra introduced by Allen (A1183). In this framework, one of the main tasks is to compute the transitive closure of a network of relations between intervals (also called path consistency in a CSPlike terminology). Almost all previous path consistency algorithms proposed in the temporal reasoning literature were based on the constraint reasoning algorithms PC1 and PC2 (Mac77). In this paper, we first show that the most efficient of these algorithms is the one which stays the closest to PC2. Afterwards, we propose a new algorithm, using the idea {open_quotes}one support is sufficient{close_quotes} (as AC3 (Mac77) does for arc consistency in constraint networks). Actually, to apply this idea, we simply changed the way compositionintersection of relations was achieved during the path consistency process in previous algorithms.
 Authors:
 LIRMM, Montpellier (France)
 Publication Date:
 OSTI Identifier:
 430683
 Report Number(s):
 CONF960876
TRN: 96:0065210058
 Resource Type:
 Conference
 Resource Relation:
 Conference: 13. National conference on artifical intelligence and the 8. Innovative applications of artificial intelligence conference, Portland, OR (United States), 48 Aug 1996; Other Information: PBD: 1996; Related Information: Is Part Of Proceedings of the thirteenth national conference on artificial intelligence and the eighth innovative applications of artificial intelligence conference. Volume 1 and 2; PB: 1626 p.
 Country of Publication:
 United States
 Language:
 English
 Subject:
 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; ARTIFICIAL INTELLIGENCE; ALGORITHMS; NETWORK ANALYSIS; DECISION MAKING
Citation Formats
Bessiere, C. A simple way to improve path consistency processing in interval algebra networks. United States: N. p., 1996.
Web.
Bessiere, C. A simple way to improve path consistency processing in interval algebra networks. United States.
Bessiere, C. Tue .
"A simple way to improve path consistency processing in interval algebra networks". United States.
doi:.
@article{osti_430683,
title = {A simple way to improve path consistency processing in interval algebra networks},
author = {Bessiere, C.},
abstractNote = {Reasoning about qualitative temporal information is essential in many artificial intelligence problems. In particular, many tasks can be solved using the intervalbased temporal algebra introduced by Allen (A1183). In this framework, one of the main tasks is to compute the transitive closure of a network of relations between intervals (also called path consistency in a CSPlike terminology). Almost all previous path consistency algorithms proposed in the temporal reasoning literature were based on the constraint reasoning algorithms PC1 and PC2 (Mac77). In this paper, we first show that the most efficient of these algorithms is the one which stays the closest to PC2. Afterwards, we propose a new algorithm, using the idea {open_quotes}one support is sufficient{close_quotes} (as AC3 (Mac77) does for arc consistency in constraint networks). Actually, to apply this idea, we simply changed the way compositionintersection of relations was achieved during the path consistency process in previous algorithms.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Dec 31 00:00:00 EST 1996},
month = {Tue Dec 31 00:00:00 EST 1996}
}

This paper continues Nebel and Burckert`s investigation of Allen`s interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P {ne} NP), in addition to their previously reported ORDHorn subclass. Furthermore, twelve tractable subclasses are identified, whose maximality is riot decided. Four of these can express the notion of sequentiality between intervals, which is not possible in the ORDHorn algebra. The satisfiability algorithm, which is common for all the algebras, is shown to be linear.

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