M. Koubarakis. The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases. Theoretical Computer Science, vol. 171, no. 1&2, 25-- 60, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....negative and non negative) Temporal constraints can express addition constraints. Hence the recognition problem for Datalog with temporal constraints is undecidable. However, an evaluation of relational calculus queries with temporal constraints is possible and is considered by Koubarakis in [19, 20]. Efficient tests for temporal constraint satisfaction are described in [9] and for monotone two variable constraints in [11] Chomicki and Imielinski [7] consider the language Datalog 1S which is like Datalog extended with an increment operator which may occur only in the first argument of ....

M. Koubarakis. The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases. Theoretical Computer Science, vol. 171, no. 1&2, 25-- 60, 1997.

....at IBM certainty: s it certain that John worked at IBM in 19907 Both calculus and algebra are extended with the operators. e ry evaluation Relational calculus: translation to relational algebra quantifier elimination (for modal queries) Complexity results for the general model [Koubarakis, 1997]: not worse than for incomplete relational databases Tractability results for a restricted model [van der Meyden, 1997] local conditions = equalities any practical temporal domain crucially depends on the number of temporal dimensions: PTIME for one dimension, co NP complete for more ....

Koubarakis, M. (1997). The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases. Theoretical Computer Science, 171 (1):89- 112.

....ranging over the reals, and u 1 ; u 2 ; un are real numbers. Notice that (1) involves only two variables, while this no longer holds for (2) This added generality may be useful in various fields such as scheduling, management of temporal databases and natural language processing ( Koubarakis, 1997, Stergiou and Koubarakis, 1998 ] Proposed four progressively more efficient algorithms for solving the consistency problem for sets of disjunctive temporal constraints. Essentially, they use (i) variations of) Smullyan s tableau procedure for propositional logic [ Smullyan, 1968 ] to ....

Manolis Koubarakis. The complexity of query evaluation in indefinite temporal constraint databases. Theoretical Computer Science, 171(1--2):25--60, 15 January 1997.

....yn are variables ranging over the reals, and u 1 ; u 2 ; un are real numbers. Notice that (1) involves only two variables, while this no longer holds for (2) This added generality may be useful in elds such as scheduling, management of temporal databases and natural language processing ([Koubarakis, 1997,Stergiou and Koubarakis, 1998] Proposed four progressively more ecient algorithms for solving the consistency problem for sets of disjunctive temporal constraints. Essentially, they use (i) variations of) Smullyan s tableau procedure for propositional logic [Smullyan, 1968] to incrementally ....

Manolis Koubarakis. The complexity of query evaluation in indefinite temporal constraint databases. Theoretical Computer Science, 171(1-2):25-60, 15 January 1997.

.... later extended to incorporate several important issues, including uncertainty in the motion and communication cost [46, 47, 48, 49, 50] Other spatio temporal models can be found in [13, 17, 18] Although a number of practical methods have been proposed for accessing and searching moving objects [19, 25, 26, 43, 48], they all require Omega Gamma n) I Os in the worst case, even if the query range is empty. Kollios et al. 23] proposed an efficient indexing scheme, based on partition trees [2, 3] for storing a set of points moving on the real line. It uses O(n) disk blocks, answers a 1 dimensional query of ....

M. Koubarakis, The complexity of query evaluation in indefinite temporal constraint databases, Theoretical Computer Science 171:25--60, 1997.

....yn are variables ranging over the reals, and u 1 ; u 2 ; un are real numbers. Notice that (1) involves only two variables, while this no longer holds for (2) This added generality may be useful in fields such as scheduling, management of temporal databases and natural language processing ([Koubarakis, 1997,Stergiou and Koubarakis, 1998] Proposed four progressively more efficient algorithms for solving the consistency problem for sets of disjunctive temporal constraints. Essentially, they use (i) variations of) Smullyan s tableau procedure for propositional logic [Smullyan, 1968] to ....

Manolis Koubarakis. The complexity of query evaluation in indefinite temporal constraint databases. Theoretical Computer Science, 171(1--2):25--60, 15 January 1997.

....extended in [37, 33, 35, 36, 34] to incorporate several important issues, including uncertainty in the motion and communication cost. Other spatio temporal models can be found in [10, 12, 13] Although a number of practical methods have been proposed for accessing and searching moving objects [35, 31, 30, 18, 19], they all require Omega Gamma n) I Os in the worst case even if the query output is O(1) Kollios et al. 16] proposed an efficient indexing scheme, based on partition trees [1, 2] for storing a set of points moving on the x axis with a fixed speed. It uses O(n) disk blocks, answers a ....

M. Koubarakis, The complexity of query evaluation in indefinite temporal constraint databases, Theoretical Computer Science 171 (1997), 25--60.

....negative and non negative) Temporal constraints can express addition constraints. Hence the recognition problem for Datalog with temporal constraints is undecidable. However, an evaluation of relational calculus queries with temporal constraints is possible and is considered by Koubarakis in [19, 20]. Efficient tests for temporal constraint satisfaction are described in [9] and for monotone two variable constraints in [11] Chomicki and Imielinski [7] consider the language Datalog 1S which is like Datalog extended with an increment operator which may occur only in the first argument of ....

M. Koubarakis. The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases. Theoretical Computer Science, vol. 171, no. 1&2, 25-- 60, 1997.

.... at IBM ffl certainty: Is it certain that John worked at IBM in 1990 BRICS Mini course on Temporal Databases 102 2 Query evaluation Relational calculus: ffl translation to relational algebra ffl quantifier elimination (for modal queries) Complexity results for the general model [Koubarakis, 1997]: ffl not worse than for incomplete relational databases Tractability results for a restricted model [van der Meyden, 1997] ffl local conditions = equalities ffl any practical temporal domain ffl crucially depends on the number of temporal dimensions: PTIME for one dimension, ....

Koubarakis, M. (1997). The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases. Theoretical Computer Science, 171(1):89-- 112.

....Section 3 to the problem of deciding the consistency of a set of (arbitrary) disjunctions of linear constraints. Previous work on this problem is reported in [2] ffl We will apply the main result of Section 3 to the problem of tractable query answering in indefinite linear constraint databases [21, 24]. Preliminary results on this topic appear in [25, 26] Acknowledgements The comments of the reviewers have greatly improved the presentation of this paper (one of them has in fact spotted a small problem with an earlier version of the algorithms VarElimination and GlobalConsistency ) ....

M. Koubarakis. The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases. Theoretical Computer Science, 171:25--60, January 1997. Special Issue on Uncertainty in Databases and Deductive Systems, Editor: L.V.S. Lakshmanan.

....from the Greek Secretariat for Research and Technology. Spiros Skiadopoulos has also been supported by a postgraduate fellowship from NATO. 1 Introduction Linear constraints have recently been used by constraint database researchers to represent temporal, spatial and spatiotemporal information [22, 13, 14, 37, 24, 31, 4, 12, 33]. The information represented by linear constraints can be of type absolute (e.g. the explosion occured at 3:30 a.m. yesterday) relative (e.g. point A is north of point B) indefinite or indeterminate (e.g. the course lasted between 1 and 2 hours) and combination of these types (e.g. point A ....

....or image and video database systems [42] It is therefore important to determine whether there exist interesting cases where query evaluation in indefinite spatiotemporal databases can be done in PTIME. In this paper we consider the scheme of indefinite constraint databases proposed by Koubarakis [25, 26, 31]. This scheme can be used to represent indefinite information arising in temporal, spatial and truly spatiotemporal applications (e.g. moving objects [40, 16] The main technical problem that we address is the discovery of tractable classes of databases and queries in this scheme. Our results ....

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M. Koubarakis. The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases. Theoretical Computer Science, 171:25--60, January 1997. Special Issue on Uncertainty in Databases and Deductive Systems, Editor: L.V.S. Lakshmanan.

.... C of linear inequalities, it might not be possible to describe the result of a variable elimination operation on C by a set of linear inequalities with size less than exponential in the number of eliminated variables (Yannakakis 1988) The following is a recent result of the authors which extends (Koubarakis 1997a) Theorem 0.2 Let C be a set of UTVPI 6= constraints. We can eliminate any number of variables from C in O(dn 4 ) time where d is the number of disequations and n is the number of variables in C. The Scheme of Indefinite Constraint Databases In this section we present the scheme of indefinite ....

....vice versa. Query evaluation over indefinite LC constraint databases can be viewed as quantifier elimination in the theory Th(M C; Th(M C; admits quantifier elimination as a consequence of the assumptions given at the beginning of this section. The following theorem is essentially from (Koubarakis 1997b) Theorem 0.3 Let DB be the indefinite LC constraint database ConstraintStore( m i=1 (8x i =D) 8t i =T i ) l j=1 Local j (x i ; t i ; j p i (x i ; t i ) and q be the query y=D; z=T : 3OE(y; z) The answer to q is (fanswer(y; z)g; where answer(y; z) is a disjunction of conjunctions of L= ....

Koubarakis, M. 1997b. The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases. Theoretical Computer Science 171:25--60. Special Issue on Uncertainty in Databases and Deductive Systems, Editor: L.V.S. Lakshmanan.

....note that we do not restrict the variables in the disjuncts to be the same pair as [DMP89] do in the framework of temporal constraint satisfaction problems. The added generality is useful in many problems including planning, scheduling [CS94] and temporal constraint databases [Kou94a, Kou94b, Kou97] 2. We have implemented four progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints (backtracking, backjumping, forward checking and forward checking with backjumping) We have also implemented the minimum remaining values heuristic in ....

M. Koubarakis. The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases. Theoretical Computer Science, 171:25--60, January 1997. Special Issue on Uncertainty in Databases and Deductive Systems, Editor: L.V.S. Lakshmanan.

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Koubarakis, M. 1997b. The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases. Theoretical Computer Science 171:25--60.

....it is Sigma p k complete. The bounds for the two theories of point constraints do not change if intervals and interval constraints are introduced. Our results will be interesting to researchers in constraint databases [KKR90] but also to the theoretical computer science community in general. In [Kou94a, Kou94b] the results of this paper are used to study the complexity of query evaluation in indefinite temporal constraint databases. In related work [Rev90] considered Datalog with integer gap order constraints (Datalog Z ) A gap order constraint is a constraint of the form: x = c; x = y; x c; c ....

Manolis Koubarakis. The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases, February 1994. Unpublished paper.

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