VLDB Journal (2005) 14: 2–29 / Digital Object Identiﬁer (DOI) 10.1007/s00778-003-0111-3
Join operations in temporal databases
, Christian S. Jensen
, Richard T. Snodgrass
, Michael D. Soo
Computer Science Department, P.O. Box 210077, University of Arizona, Tucson, AZ 85721-0077, USA
Department of Computer Science, Aalborg University, Fredrik Bajers Vej 7E, 9220 Aalborg Ø, Denmark
Amazon.com, Seattle; e-mail: email@example.com
Edited by T. Sellis. Received: October 17, 2002 / Accepted: July 26, 2003
Published online: October 28, 2003 –
Abstract. Joins are arguably the most important relational
operators. Poor implementations are tantamount to comput-
ing the Cartesian product of the input relations. In a temporal
database, the problem is more acute for two reasons. First, con-
ventional techniques are designed for the evaluation of joins
with equality predicates rather than the inequality predicates
prevalent in valid-timequeries. Second, the presence of tempo-
rally varying data dramatically increases the size of a database.
These factors indicate that specialized techniques are needed
to efﬁciently evaluate temporal joins.
We address this need for efﬁcient join evaluation in tempo-
ral databases. Our purpose is twofold. We ﬁrst survey all previ-
ously proposed temporal join operators. While many temporal
join operators have been deﬁned in previous work, this work
has been done largely in isolation from competing propos-
als, with little, if any, comparison of the various operators.
We then address evaluation algorithms, comparing the appli-
cability of various algorithms to the temporal join operators
and describing a performance study involving algorithms for
one important operator, the temporal equijoin. Our focus, with
respect to implementation, is on non-index-based join algo-
rithms. Such algorithms do not rely on auxiliary access paths
but may exploit sort orderings to achieve efﬁciency.
Keywords: Attribute skew – Interval join – Partition join –
Sort-merge join – Temporal Cartesian product – Temporal join
– Timestamp skew
Time is an attribute of all real-world phenomena. Conse-
quently, efforts to incorporate the temporal domain into
database management systems (DBMSs) have been ongo-
ing for more than a decade [39,55]. The potential beneﬁts of
this research include enhanced data modeling capabilities and
more conveniently expressed and efﬁciently processed queries
Whereas most work in temporal databases has concen-
trated on conceptual issues such as data modeling and query
languages, recent attention has been on implementation-
related issues, most notably indexing and query processing
strategies. In this paper, we consider an important subproblem
of temporal query processing, the evaluation ad hoc temporal
join operations, i.e., join operations for which indexing or sec-
ondary access paths are not available or appropriate. Temporal
indexing, which has been a proliﬁc research area in its own
right , and query evaluation algorithms that exploit such
temporal indexes are beyond the scope of this paper.
Joins are arguably the most important relational operators.
This is so because efﬁcient join processing is essential for the
overall efﬁciency of a query processor. Joins occur frequently
due to database normalization and are potentially expensive to
compute . Poor implementations are tantamount to com-
puting the Cartesian product of the input relations. In a tem-
poral database, the problem is more acute. Conventional tech-
niques are aimed at the optimization of joins with equality
predicates, rather than the inequality predicates prevalent in
temporal queries . Moreover, the introduction of a time
dimension may signiﬁcantly increase the size of the database.
These factors indicate that new techniques are required to ef-
ﬁciently evaluate joins over temporal relations.
This paper aims to present a comprehensive and systematic
study of join operations in temporal databases, including both
semantics and implementation. Many temporal join operators
have been proposed in previous research, but little compari-
son has been performed with respect to the semantics of these
operators. Similarly, many evaluation algorithms supporting
these operators have been proposed, but little analysis has ap-
peared with respect to their relative performance, especially
in terms of empirical study.
The main contributions of this paper are the following:
• To provide a systematic classiﬁcation of temporal join op-
erators as natural extensions of conventional join opera-
• To provide a systematic classiﬁcation of temporal join
evaluation algorithms as extensions of common relational
query evaluation paradigms.
• To empirically quantify the performance of the temporal
join algorithms for one important, frequently occurring,
and potentially expensive temporal operator.