M. Yannakakis. Graph-theoretic methods in database theory. In Proc. of the Symp. on Princ. of Database Syst., pages 230--242, 1990. 15  Home/Search   Document Not in Database   Summary   Related Articles   Check

....as a valid connection between s and t if the word spelled out by P (i.e. the concatenation, in order, of the labels on the edges of P ) is in a certain language. When the filter language is a context free language, this is called CFL reachability, a concept originated by Yannakakis in 1990 [51]. CFL reachability problems can be solved in time cubic in the number of nodes in the graph (and, in general, no algorithm with a better running time is known) For a survey of ways in which CFLreachability applies to program analysis problems, see [38] A slight clash in terminology exists. In ....

....problems, they run in linear time and use linear space. Although the authors became aware of the connection to the more general concept of CFL reachability sometime in the fall of 1994, of the papers from this period, only [36] mentions CFLreachability explicitly and references Yannakakis s paper [51]. Sagiv, Reps, and Horwitz used similar ideas but went beyond just CFL reachability to give more powerful, but still cubic time, interprocedural dataflow analysis algorithms [44] Among other benefits, this work showed how to obtain precise jump functions for certain classes of ....

M. Yannakakis. Graph-theoretic methods in database theory. In Symp. on Princ. of Database Syst., pages 230--242, 1990.

.... Related previous work Estimation of order statistics and outliers [ARS97, AS95, JC85, RML97, Olk93] has received much attention in in the context of sorting [DNS91] selectivity estimation [PIHS96] query optimization [SALP79] and in providing online user feedback [Hel] The survey by Yannakakis [Yan90] is a comprehensive account of graph theoretic methods in database theory. Classical work on time space tradeoffs [Cob66, Tom80] may be interpreted as lower bounds on workspace for problems such as verifying palindromes, perfect squares and undirected st connectivity. Paterson and Munro [MP80] ....

M. Yannakakis. Graph-theoretic methods in database theory. Proc. PODS, 230--242, 1990.

....algorithm [2, 14, 4, 3, 9, 10, 12] The improved e#ciency of the rewritten program is due to the fact that it restricts the search to the portion of the underlying database that is relevant to the query. Other techniques present special algorithms that compute directly the original program [7, 17, 1, 6, 18]. Rewriting based techniques can be classified according to their generality. Techniques that can be applied to all programs include the magic set method and the supplementary magic set method [2, 4] Specialized techniques include the factorization and reduction of programs [9] the combination ....

.... the left and the right parts of the query graph: thus, for each arc in the right part of the graph (accessed at cost hB (m) O(m) arcs are selected from the left part, where the cost for each arc is also hB (m) Therefore the global cost is ) Yannakakis Method: The method proposed in [18] improves the computation of the fixpoint for chain programs, i.e. programs with binary predicates not containing shared variables. This method has complexity n ) In the present form, the method has very limited practical interest due to the fact that it does not make use of the bound ....

M. Yannakakis. Graph-Theoretic Methods in Database Theory. In Proc. of the Ninth ACM PODS, 1990, pp 230--242.

....thus resulting in rather ine#cient query executions. Therefore, as chain queries are rather frequent in practice (e.g. graph applications) there is a need for specialized optimization methods. Indeed, several specialized methods for chain queries have been proposed in the literature (e.g. in [1, 7, 9, 11, 35, 36]) Unfortunately, these methods do not fully exploit the query bindings. On the other hand, the counting method is very e#ective for chain queries with bindings, for many chain queries whose recursive rules are linear; however, this method, although proposed in the context of general queries [29] ....

....to perform a set oriented computation [34] Also, this method does not take advantage of all possible chain structures but it does exploit possible bindings. The first method that is specialized for chain queries and also based on the properties of context free language is due to Yannakakis [36], who proposed a dynamic programming technique for implementing a procedure to recognize strings for general context free languages that was originally due to Cocke Younger and Kasami [3] This technique turns out to be e#cient for unbound queries, but does not support any mechanism to reduce the ....

M. Yannakakis. Graph-Theoretic Methods in Database Theory. In Proceedings of the Ninth ACM Symposium on Principles of Database Systems, 1990, pages 230--242.

....thus resulting in rather ine#cient query executions. Therefore, as chain queries are rather frequent in practice (e.g. graph applications) there is a need for ad hoc optimization methods. Indeed, various specialized methods for chain queries have been proposed in the literature (e.g. in [1, 5, 8, 22]) Unfortunately, these methods do not fully exploit possible bindings. To find a method that is particularly specialized for bound chain queries, we have to go back to the counting method; however, this method, although proposed in the context of general queries [17] preserves the original ....

....to perform a set oriented computation. Also this method does not take advantage from a possible chain structure but it does exploit possible bindings. The first proposal of a method that is both specialized for chain queries and based on the properties of context free language is due to Yannakakis [22], who has proposed a dynamic programming technique implementing the method of Cocke Younger and Kasami to recognize strings of general context free languages [3] This technique turns out to be e#cient for unbound queries but it does not support any mechanism to reduce the search space when ....

M. Yannakakis. Graph-Theoretic Methods in Database Theory. In Proc. Ninth ACM Symposium on Principles of Database Systems, 1990, pages 230--242.

....Q2, 99 of the database is discarded during ltering for both values of l p . For the 16,000 molecules database, 640 subgraphs are found for Q1 and 612 for Q2. is proportional to the query size. As expected, p decreases substantially with larger l p , but not always. 3. 3 Subgraph Matching In [105] Yannakakis surveyed traditional graph searching problems with applications to data management, including computing transitive closures, recursive queries, and the complexity of path searching in databases. We review here some classical subgraph matching techniques, mostly having to do with step 3 ....

M. Yannakakis. Graph theoretic methods in database theory. In Proceedings of the ACM SIGMOD SIGACT SIGART Symposium on Principles of Database Systems, pages 230-242, 1990.

....regular expression is shown to be NP complete in the size of the graph, and tractable subcases are identified. Cycle constraints which restrict cycles in a graph by regular expressions are also discussed. Path queries (regular, 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 ....

M. Yannakakis. Graph-theoretic methods in database theory. In Proc. ACM Symp. on Principles of Database Systems (invited talk), pages 230--242, 1990. 32

.... 2 C i : v is a call node [15] for each (b; x) such that ( b; e 0 ) b; x) B 0 ) 2 SummaryEdges do [16] Propagate(e (b; x) B B 0 ) 17] od [18] end case [19] case v = x 2 O i : v is an exit node [20] for each pair (b; j) 2 callers(i) do b 2 B j and Y j (b) i [21] if there is no pair of the form ( b; e) b; x) B 0 ) in SummaryEdges then [22] Insert ( b; e) b; x) B) into SummaryEdges [23] else if ( b; e) b; x) B 0 ) 2 SummaryEdges B = true B 0 = false then [24] SummaryEdges : SummaryEdges Gamma f( b; e) b; x) B 0 )g) f( b; ....

.... fl 1 ; p(fln ) fl n) 18] Sat(M i ; c; fl) Nodes1(M i ,fl) S (fi;ffi)2SPLIT(fl) c(Effi(p(fl 1 ) fl 1 ; p(fl n ) fln ) true Nodes2 (M i ,fi) 19] for each b 2 Boxes(M i ) do [20] P (b;i;c) Y i (b) c 0 ) such that 8fl 2 F : c 0 (fl) true iff (b; x) 2 Sat(M i ; c; fl) [21] CONT = OLDCONT [fP (b;i;c) g [22] od [23] od [24] od [25] Now build the output HSM M [26] M = fM i;c j(M i ; c) 2 CONT g [27] Forall 1 i n, for all c 2 CONT, 28] M i;c = N i Theta fcg; B i Theta fcg; I i Theta fcg; O i Theta fcg; X 0 i;c ; Y 0 i;c ; C 0 i;c ; R i Theta ....

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M. Yannakakis. Graph-theoretic methods in database theory. In Proc. of the Symp. on Princ. of Database Syst., pages 230--242, 1990.

....polymorphic ow analysis. The main contributions of this paper are: A novel presentation of polymorphic subtyping, using instantiation constraints (also known as semiuni cation constraints [Hen93] Based on this presentation, we are able to apply Context Free Language (CFL) Reachability [Yan90, RHS95, MR00] techniques to compute directional, context sensitive ow information for higher order programs in polymorphic subtyping systems (including polymorphic recursion) Our resulting algorithm improves the asymptotic complexity of the best previously known algorithm [Mos96] based on polymorphic ....

Mihalis Yannakakis. Graph-theoretic methods in database theory. In Proceedings of the 9th ACM Symposium on Principles of Database Systems, pages 230-242, 1990. A Higher-order example

....graphs, we show that (i) the problem of finding a regular language constrained simple path between source and destination is solvable in polynomial time and (ii) the extension to finding context free language constrained simple paths is NP complete. Our results extend the previous results in [MW95, SJB97, Ya90]. Several additional extensions and applications of our results in the context of transportation problems are presented. For instance, as a corollary of our results, we obtain a polynomial time algorithm for the BEST k SIMILAR PATH problem studied in [SJB97] The previous best algorithm was ....

....detailed account of the TRANSIMS project. Regular expression constrained simple path problems were 4 considered by Mendelzon and Wood [MW95] The authors investigate this problem in the context of finding efficient algorithms 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 ....

[Article contains additional citation context not shown here]

M. Yannakakis "Graph Theoretic Methods in DataBase Theory," invited talk, Proc. 9th ACM SIGACT-SIGMOD-SIGART Symposium on Database Systems (ACM-PODS), Nashville TN, 1990, pp. 230-242.

....since most queries on right linear programs are likely to have multiple initial values. Overbound Queries To motivate partial sips, consider the transitive closure query t(u; v) with both arguments bound. The transitive closure program can be written in a right linear fashion. Yannakakis [Yan90] shows that when computing a transitive closure, it is not profitable to use both destination and source bindings. Only one of the bindings can be used, and the interesting question for such queries is: do we search from the given source values, or do we search from the given destination values ....

....sources and destinations: Qc) init(X; Y ) anc bb (X;Y ) Let there be t = O(n 2 ) tuples in the initial set init, with t1 = O(n) different sources, and t2 = O(n) different destinations. As discussed in Section 1, query Qc contains more bindings than can be effectively used. Yannakakis [Yan90] shows that a full transitive closure (anc ff ) can be computed in time O(ne) where n is the number of nodes, and e is the number of edges (number of tuples in par) A single source transitive closure can be computed in time O(e) so if we have t1 sources, we should be able to compute the ....

Mihalis Yannakakis. Graph-theoretic methods in database theory. In Proceedings of the Ninth Symposium on Principles of Database Systems (PODS), pages 230--242, Nashville, TN, April 24 1990. ACM SIGACT-SIGMOD-SIGART.

....can be solved using a dynamic programming algorithm. The algorithm can be thought of as a generalization of the CYK algorithm for context free recognition [7, 16] There is a general result that all CFL reachability problems can be solved in time cubic in the number of vertices in the graph [15]. Because the number of vertices in the ADDG for a program p is bounded by O(P V ar Ops) where P is the number of parameters in p, V ar is the number of where variables in p, and Ops is the number of cons car cdr operations in p, the problem of identifying whether an L path exists from every ....

.... dependency graph with new nodes and new edge markings and we use CFL reachability rather than a closed semi ring graph algorithm [1, 3] ffl There is a general result that all context free language reachability problems can be solved in time cubic in the number of vertices in the graph [15]. This allows us to obtain a cubic time bound for our algorithm. Andersen and Holst did not report a bound on the running time of their algorithm, although we suspect that for the class of problems we are addressing, their methods would also run in cubic time. ffl We are able to provide a ....

M. Yannakakis. Graph-theoretic methods in database theory. In Proceedings of the Symposium on Principles of Database Systems, 1990, pages 230--242, 1990.

....the contents and structure of a database. Second, a graph representation has the advantage that graph theoretic algorithms and proofs may be applied to extract and derive properties of the graph. There are many examples of graph related applications that can assist in solving query processing [Yan90] and object data management problems such as type inferencing, optimization strategies for object distribution and dynamic schema evolution. a) Atomic value. R i . ....

M. Yannakakis. Graph-Theoretic Methods in Database Theory. In Proc. of the 9th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 230--242, Nashville, Tenn., April 1990.

....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]. ....

M. YANNAKAKIS, Graph-theoretic methods in database theory, in Proceedings of the 9th ACM SIGACTSIGMOD -SIGART Symposium on Principles of Database Systems, Nashville, Tenn., Apr. 2--4, 1990, ACM, New York, pp. 230--242.

....name: M. Rauch The fully dynamic version of the problem allows both insertions and deletions of edges. It is harder than the versions that allow only insertions or only deletions. Dynamic graph algorithms have applications in communication networks, computer aided design [2] database systems [20], logic programming [3] and incremental data flow analysis [4] Frederickson [9] gave an algorithm for maintaining 2 edge connected components in a graph which takes O( p m) time per update, where m is the number of edges in the graph. This bound was consequently reduced to O( p n) by ....

M. Yannakakis, "Graph Theoretic Methods in Database Theory" Proc. of the ACM Conference on Principles of Database Systems, 1990, 230--242.

.... views over their content) Problems that have been revisited due to the Introduction 2 WebOQL: Exploiting Document Structure in Web Queries popularity of the Web include: querying structured documents [AC 97, CA 94, GZC89] querying semistructured data [AQ 96, BD 96] and querying graphs [MW95, Yan90]. Many systems and languages have been proposed for solving each of these Web data management problems, but none of these systems provides a framework for approaching the problems from a unified perspective. In this thesis we present the WebOQL system, whose goal is to provide such a framework. ....

....has not been yet added. Alternatively, if we view both T and G h,w as finite automata accepting languages L 1 and L 2 respectively, procedure Search can be seen as performing a depth first search of the automaton accepting L 1 L 2 1 . The states for this intersection automaton [Yan90] are pairs (x, s) consisting of a node x in G h,w and a state s in T, and there is a transition from a state (x, s) to another state (y, t) if G h,w has an edge labeled r from x to y, T has a transition labeled p from s to t and p(r) is true. In procedure Search, the states and the ....

M. Yannakakis, Graph-theoretic methods in database theory, in Proc. of 9th. ACM Symp. on PODS, Nashville, pp. 230-242, 1990. 72 WebOQL: Exploiting Document Structure in Web Queries

....depending on the representation and the techniques used. Hybrid algorithms utilize the optimizing features of graph algorithms in a matrix framework. Most algorithms on graphs solve a variety of problems involving path computations such as, critical path, shortest path, bill of materials etc [Yan90] We are interested in solving the reachability problem on the dependence graph for the purpose of potential implicit update precomputation. For the time being, we will restrict ourselves to studying the problem of computation and incremental update of transitive closure in primary storage. That ....

M. Yannakakis. Graph Theoretic Methods in Database Theory. In ACM PODS, pages 230--242, 1990.

....n, we wish to determine if G can generate w. The classic C K Y algorithm for this problem requires O(n 3 ) time. Using fast matrix multiplication, Valiant [14] was able to slightly improve the asymptotic bound, but his algorithm is highly impractical. A related problem is CFL reachability ([15, 11]) where for a fixed grammar G, we are given a directed, edge labeled, graph H , having size n, with designated source and target nodes s and t, and we wish to determine whether s can reach t in H via a path labeled by a string in L(G) CFL membership is the special case of this problem where H is ....

....wish to determine whether s can reach t in H via a path labeled by a string in L(G) CFL membership is the special case of this problem where H is just a simple path labeled by w. Unlike CFL membership, CFL reachability is P complete, and the best known algorithms require Omega (n 3 ) time ([15]) Using the close correspondence between recursive automata and context free grammars, a grammar G can be translated to a recursive automaton AG . To test CFL reachability, we can take the product of AG with H , and check for reachability. The product has size O(n) with O(n) entry nodes per ....

M. Yannakakis. Graph-theoretic methods in database theory. In Proc. 9th ACM Symp. on Principles of Database Systems, pages 230--242, 1990.

....in the same state) and on d it decrements the counter if it was positive and rejects the whole input if the counter was 0. The machine accepts if after processing the input word it has seen some b and the counter is 0. Thus, the language L inf is context free. Thus we can adopt the algorithm of [Yan90] for computing the L transitive closure of context free languages. The algorithm is derived from a context free grammar for L inf in Chomsky normal form. We will describe now in more concrete terms the algorithm for our case. It uses the following grammar: A a j b j AA j A 0 d A 0 c j ....

M. Yannakakis. Graph-theoretic methods in database theory. In Proceedings of the 9th ACM Symposium on Principles of Database Systems, pages 230--242, 1990.

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M. Yannakakis. Graph-theoretic methods in database theory. In Proc. of the Symp. on Princ. of Database Syst., pages 230--242, 1990. 15

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M. Yannakakis. Graph-theoretic methods in database theory. In Proc. of the Symp. on Princ. of Database Syst., pages 230--242, 1990.

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M. Yannakakis. Graph-theoretic methods in database theory. In Proceedings of the Symposium on Principles of Database Systems, pages 230--242, 1990.

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M. Yannakakis. Graph-theoretic methods in database theory. In Proceedings of the ACM Symposium on Principles of Database Systems, pages 230--242, 1990.

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M. Yannakakis. Graph-theoretic methods in database theory. In PODS: Principles of Database Systems, pp. 203--242. ACM, 1990.

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M. Yannakakis. Graph-theoretic methods in database theory. In PODS: Principles of Database Systems, pp. 203--242. ACM, 1990.

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