A.Buchsbaum, P.C.Kanellakis, and J.S.Vitter. A data structure for arc insertion and regular path finding. Annals of Math. and AI, 3:187--210, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....boundedness problem for regular path expressions. We show that it is decidable whether a given regular path query is equivalent to a path query without recursion, assuming that a given set of equalities among words is satisfied. Related work Path queries in graphs have been studied formally in [10, 12, 8, 24]. The language Graphlog, introduced in [12] expresses queries using graph patterns, where paths are specified by regular expressions. Graphlog is shown equivalent to stratified linear Datalog and other languages. The complexity of path queries in graphs is studied in [24] Specifically, the ....

....linear and context free) and their complexity are also considered in [32] It is shown there how regular path queries on graphs can be reduced to the transitive closure query using the cross product of the input graph with the query automaton. Connections with Datalog are also discussed. In [8], the problem of finding paths in a labeled graph that spell some word in a regular language is considered. They propose a data structure that can be incrementally maintained when arcs are inserted and deleted. The problem is different from ours (the regular language is fixed and the focus is on ....

[Article contains additional citation context not shown here]

A.Buchsbaum, P.C.Kanellakis, and J.S.Vitter. A data structure for arc insertion and regular path finding. Annals of Math. and AI, 3:187--210, 1991.

....of mediators is presented by Zhou and Hull in [ZH96] Other Incremental algorithms have also been studied in a number of other areas. These include: reasoning about changes [Kuc91, UO92] distributed computing [AISN90, Ita91] programming languages [SH91, TR81] maintenance of graph properties [BKV90, CC82] and maintenance of other data structures [CH91, Jag90, KP81, LHM 86] A study of methods for incremental database query computation is provided elsewhere [Vis94] Chapter 2. A Survey on View Maintenance: Applications and Techniques 16 2.5 Algorithms for Incremental View Maintenance ....

....deletions of edges. Furthermore, they showed that recursive queries in general cannot be maintained in languages with the expressive power of SQL (excluding, of course, SQL3 which supports recursion) The problem of maintaining transitive closures has also been studied [CC82, CH91, Jag90, Jak92, BKV90, AISN90] Chapter 2. A Survey on View Maintenance: Applications and Techniques 20 Reasoning Methods A method for computing changes in predicates defined in safe stratified Datalog is presented by Urp i and Oliv e [UO92] Their method is based on the notion of events: external events are ....

A.L. Buchsbaum, P.C. Kanellakis, and J.S. Vitter. A Data Structure for Arc Insertion and Regular Path Finding. In 1st Annual ACM-SIAM Symposium on Discrete Algorithms, pages 22--31, 1990.

.... UO92] integrity constraint verification [CW90, Ple93] alerting [BC79] and active database systems [BA93, GJS92] More remote work on incremental techniques includes work on distributed computing [AISN90, Ita91, WDSY91] programming languages [SH91, TR81] maintenance of graph properties [BKV90, CC82] and maintenance of other data structures [CH91, Jag90, KP81, LHM 86] A study of methods for incremental database query computation appears in [Vis94] The rationale behind the development and use of incremental algorithms to solve the problem of updating a query answer once the ....

A.L. Buchsbaum, P.C. Kanellakis, and J.S. Vitter. A Data Structure for Arc Insertion and Regular Path Finding. In 1st Annual ACM-SIAM Symposium on Discrete Algorithms, pages 22--31, 1990.

....for processing database queries (see [CMW87, CMW88, MW95] Yannakakis [Ya90] in his keynote talk has independently outlined some of the polynomial time algorithms given in Section 5. However, the emphasis in [Ya90] was on database theory. Online algorithms for regular path finding are given in [BKV91]. Our work on finding formal language constrained shortest paths is also related to the work of Ramalingam and Reps [RR96] The authors were interested in finding a minimum cost derivation of a terminal string from one or more non terminals of a given context free grammar. The problem was first ....

A. Buchsbaum, P. Kanellakis and J. Vitter, "A Data Structure for Arc Insertion and regular Path Finding," Proc. 1st ACM-SIAM Symposium on Discrete Algorithms (SODA), 1990, pp. 22-31.

....k is the number of states of a finite automaton for a regular language. With the new fully dynamic transitive closure algorithm presented here, each new relation can be inserted in O(k(nk) 2 log(kn) time. Each deletion of a relation can be accomplished in O( nk) 2 log(kn) time. See also [2]. In [5] the question of maintaining distances between objects in a very large data base is posed. Reps and others have investigated the application of dynamic shortest paths and transitive closure algorithms to data flow analysis and compilers. See [13] 2. Exact all pairs shortest paths for ....

A. Buchsbaum, P. Kanellakis, and J. Vitter. A data structure for arc insertion and regular path finding,. Annals of Mathematics and Artificial Intelligence, 3:187--210, 1991.

....materialized views upon updates. It is also closely related to the problem of partially evaluating definite logic programs [27] Finally, when restricted to standard transitive closure programs, our task can be viewed as solving the incremental transitive closure computation problem for graphs [10, 14, 20, 21]. More detailed comparison will be given in Section 6. In general, all these optimization approaches store extra information to reduce the time required for subsequent computations. In our case, we store the answer to the query in one database state (and possibly additional derived facts) to ....

A.L. Buchsbaum, P.C. Kanellakis and J.S. Vitter. A data structure for arc insertion and regular path finding. In Proc. ACM-SIAM Symp. on Discrete Algorithms, 1990.

....materialized views upon updates. It is also closely related to the problem of partially evaluating definite logic programs [26] Finally, when restricted to standard transitive closure programs, our task can be viewed as solving the incremental transitive closure computation problem for graphs [10, 14, 19, 20]. More detailed comparison will be given in Section 6. In general, all these optimization approaches store extra information to reduce the time required for subsequent computations. In our case, we store the answer to the query in one database state (and possibly additional derived facts) to ....

A.L. Buchsbaum, P.C. Kanellakis and J.S. Vitter. A data structure for arc insertion and regular path finding. In Proc. ACM-SIAM Symp. on Discrete Algorithms, 1990.

....on the expressive power of graph based query languages in which the restriction of simple path semantics is dropped. One such language that captures exactly the queries computable in nondeterministic logarithmic space is presented in [8] On line algorithms for regular path finding are given in [5], while a survey of many results can be found in [24] ....

A. BUCHSBAUM, P. KANELLAKIS, AND J. VITTER, A data structure for arc insertion and regular path finding, in Proceedings of the 1st ACM-SIAM Symposium on Discrete Algorithms, 1990, pp. 22--31.

....boundedness problem for regular path expressions. We show that it is decidable whether a given regular path query is equivalent to a path query without recursion, assuming that a given set of equalities among words is satisfied. Related work Path queries in graphs have been studied formally in [8, 10, 6, 20]. The language GraphLog, introduced in [10] expresses queries using graph patterns, where paths are specified by regular expressions. GraphLog is shown equivalent to stratified linear Datalog and other languages. The complexity of path queries in graphs is studied in [20] Specifically, the ....

....and other languages. The complexity of path queries in graphs is studied in [20] Specifically, the problem of finding all pairs of nodes connected by a simple path satisfying a given regular expression is shown to be NP complete in the size of the graph, and tractable subcases are identified. In [6], the problem of finding paths in a labeled graph that spell some word in a regular language is considered. They propose a data structure that can be incrementally maintained when arcs are inserted and deleted. The problem is different from ours (the regular language is fixed and the focus is on ....

[Article contains additional citation context not shown here]

A.Buchsbaum, P.C.Kanellakis, and J.S.Vitter. A data structure for arc insertion and regular path finding. Annals of Math. and AI, 3:187--210, 1991.

.... no better bound than O( p m ) is known for the corresponding fully dynamic problems [11] Moreover, despite intensive research on dynamic problems on graphs (such as dynamic maintenance of connectivity [7, 8, 10, 11, 14, 20, 22, 29, 30] 2 and 3 connectivity [7, 12, 29, 30] transitive closure [3, 4, 15, 16, 17, 18, 19, 31], planar graphs [6, 7, 19, 25] shortest paths [2, 9, 21, 24, 31] and minimum spanning trees [5, 8, 11, 24] there are very few graphtheoretic problems for which a fully dynamic non trivial algorithm is known. As mentioned in [30] the fully dynamic maintenance of the connected components of a ....

A. L. Buchsbaum, P. C. Kanellakis, and J. S. Vitter, "A data structure for arc insertion and regular path finding", Proc. 1st Annual ACM-SIAM Symp. on Discrete Algorithms, 1990, 22--31.

....algorithms were presented which improve this result. A data structure for arbitrary digraphs that support edge insertions in amortized O(n) time, queries in O(1) time, and use O(n 2 ) space are given in [64] An extension of this result to finding regular paths for a regular language is given in [14]. A semi dynamic algorithm for acyclic digraphs that support edge deletions in in amortized O(n) time, queries in O(1) time, and use O(n 2 ) space is presented in [65] La Poutr e and van Leeuwen [85] present two semi dynamic data structures supporting transitive closure on general digraphs. The ....

A.L. Buchsbaum, P.C. Kanellakis, and J.S. Vitter, "A Data Structure for Arc Insertion and Regular Path Finding," Proc. ACM-SIAM Symp. on Discrete Algorithms (1990), 22--31.

....in our setting equivalence classes are distinguished by path queries, while in their setting they are distinguished by first order formulas. Hence the language equivalences are coarser than FO equivalences, and result in fewer equivalence classes. Buchsbaum, Kanellakis, and Vitter consider in [5] the problem of incrementally maintaining query paths given by a fixed regular expression under either database insertions or deletions (but not both) They describe an efficient method for incremental updates. Since their method refers to a fixed regular expression, it could be used in ....

Adam Buchsbaum, Paris Kanellakis, and Jeffrey Scott Vitter. A data structure for arc insertion and regular path finding. Annals of Mathematics and Artificial Intelligence, 3:187--210, 1991.

....path from u to v) However, in the dynamic realm the problem seems much harder. The best previously known dynamic results for general digraphs are semi dynamic data structures with O(n 2 ) space, constant query time, and O(n) update time. Data structures that support insertions only are given in [12,50,84]. Data structures that are restricted to acyclic digraphs and support only deletions can be found in [12,51] We can obtain better results if we restrict ourselves to specific classes of graphs. For series parallel digraphs, Italiano, Marchetti Spaccamela, and Nanni [52] gave an O(n) space data ....

....results for general digraphs are semi dynamic data structures with O(n 2 ) space, constant query time, and O(n) update time. Data structures that support insertions only are given in [12,50,84] Data structures that are restricted to acyclic digraphs and support only deletions can be found in [12,51]. We can obtain better results if we restrict ourselves to specific classes of graphs. For series parallel digraphs, Italiano, Marchetti Spaccamela, and Nanni [52] gave an O(n) space data structure that handles both queries and updates in O(log n) time. For the class of planar st graphs (acyclic ....

A.L. Buchsbaum, P.C. Kanellakis, and J.S. Vitter, "A data structure for arc insertion and regular path finding," Proc. ACM-SIAM Symp. on Discrete Algorithms (1990), 22--31.

....are only superficially related to the FO equivalence classes: the queries we consider to distinguish between two tuples are only chain queries. Hence the language equivalences are coarser than FO equivalences, and results in fewer equivalence classes. Buchsbaum, Kanellakis, and Vitter consider in [5] the problem of incrementally maintaining query paths given by a fixed regular expression under either database insertions or deletions (but not both) They describe an efficient method for incremental updates. Since their method refers to a fixed regular expression, it could be used in ....

Adam Buchsbaum, Paris Kanellakis, and Jeffrey Scott Vitter. A data structure for arc insertion and regular path finding. Annals of Mathematics and Artificial Intelligence, 3:187--210, 1991.

....but by using joins and appropriate indexes on the tables, it is not too expensive to maintain the tables and compute the impact on the entire path. When more complex paths are considered (with wild cards and regular expressions) we plan to evaluate more complex techniques such as those in [BKV91] To conclude this section, it should be observed that many other aspects complicate the incremental maintenance of a materialized OEM view. We focused the discussion on the maintenance of inverse path expressions because this single point introduces a new dimension to the problem. 5 Conclusion ....

A. Buchsbaum, P.C. Kanellakis, and J.S. Vitter. A data structure for arc insertion and regular path finding. Annals of Math. and AI, 3:187--210, 1991.

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