Graph Programming: Tools and Techniques

Transcription

1 Graph Programming: Tools and Techniques Literature Review Seminar Chris Bak The University of York January 19, 2012 Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

2 Outline The Current GP System Other Graph Programming Tools Graph Matching Rooted Graph Transformation Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

3 GP Intended to be a simple high-level graph programming language. Has a GUI, simple syntax and formal semantics. Quite efficient, although improvements can be made. Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

4 Conditional Rule Schemata Used to specify a standard graph transformation rule with an optional condition. Variables, tags and conditions are used to enhance rules. addcost(a,n,x,y:int) x:n a where a 0 y a x:n y:n+a Individual rules combined with control constructs to create programs. Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

5 System Overview Graphs, rules and programs are created in the graphical editor. These are compiled to bytecode which is fed into the York Abstract Machine (YAM). Diagram from The Graph Programming Language GP (Plump, 2009) Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

6 The YAM Low level machine that performs operations on graphs by executing generated bytecode. (Manning and Plump, 2008) Stack based architecture to control backtracking. Only the current graph is stored in the machine, the graph change stack records instructions to be executed to revert back to previous graphs. The choice stack saves machine states whenever a choice is made, including the number of graph changes. Nondeterminism handled by executing operations in textual order. Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

7 PROGRES One of the first graph programming languages. Programs are written textually, but PROGRES provides a GUI for viewing program output. Uses an object-oriented style of attributes, classes and inheritance for nodes and edges. Allows optional node matching in a rule. Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

8 AGG AGG has a GUI which allows the user to create rules and graph grammars. Items can be typed and attributed according to pre-defined Java classes or user defined ones. AGG also allows rules to change such attributes with Java methods in addition to simple expressions. Solves graph matching by transforming it into a constraint satisfaction problem and applying well studied CSP algorithms. (Rudolf, 1998) Offers critical pair analysis and graph parsing. Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

9 GrGEN Currently the fastest graph transformation tool. Like PROGRES, programs must be written textually but has a GUI for viewing graphs. Large syntax which provides many features but more error prone. Claims to have formal semantics, but they are incomplete due to the large size of the language. Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

10 Sierpinski benchmark Generation of Sierpinski Triangles: A Case Study for Graph Transformation Tools, Proc. AGTIVE 2007, LNCS Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

11 Graph matching in GP Subgraph matching is the bottleneck for graph transformation tools. Matching a pattern P in a host graph H has a worst case time of H P. Often implemented as a searchplan; an ordering of primitive matching operations. GP has a static searchplan, prioritising operations with the least amount of nondeterminism. (Manning and Plump, 2008) For example, matching edges whose source and/or target has already been matched takes priority over matching a node. Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

12 Searchplan generation in PROGRES Computes a searchplan by constructing a plan graph for the LHS of a rule. Greedily traverses through the plan graph to find the cheapest searchplan with respect to the following cost function CostSum(Op 1,..., Op n ) = n BaseCosts(Op i ) NoTrials SP (i) i=1 BaseCosts(Op) has a fixed value for each primitive operation. NoTrials SP (i) estimates the number of trials the first i operations of the searchplan will take. More details in Graph Pattern Matching in PROGRES (Zündorf, 1996). Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

13 Searchplan generation in GrGEN The idea of this algorithm is to reduce the choice of node/edge matches as much as possible. Only two primitive operations in GrGEN: lkp(x) and ext(v, e) (where node v is incident to edge e). The host graph is analysed to calculate the costs of each primitive operation. The cost of lkp(x) is the number of corresponding (same label) items in G. The cost of ext(v, e) is (approximately) the number of corresponding edges in G incident to a corresponding node. Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

14 Searchplan generation in GrGEN A plan graph is constructed from the LHS L of the rule. Apart from the root node, the nodes of the plan graph (p-nodes) represent a node or edge in L. Edges in the plan graph represent a primitive operation, labelled with the cost of that operation. The root node is connected to all other p-nodes by an lookup edge. p-nodes representing an edge are connected to p-nodes representing its source and target by p-edges labelled accordingly. Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

15 Searchplan generation in GrGEN L v 1 x e 1 a v 2 y > X v 1 e 1 v 2 * * * Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

16 Searchplan generation in GrGEN Once the plan graph has been constructed, a minimum spanning arborescence (MSA) is found. This is equivalent to finding the (unordered) set of primitive operations with the least cost. Ordering the set is relatively straightforward, a best-first traversal of the MSA starting at the root node. This is all done at runtime! Algorithm comprehensively described in An Optimization Technique for Subgraph Matching Strategies (Batz, 2006). Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

17 Rooted Graph Transformation A unique root node is chosen in the LHS of a rule and in the host graph. These are matched immediately at the start of the graph matching process. Assuming the LHS is connected and nodes in the host graph have a bounded outdegree, matching is done in constant time. (Dodds and Plump, 2006) This technique has been used to efficiently check shape safety of pointer structures in C using rooted graph reduction rules. (Dodds and Plump, 2005) Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

18 Rooted Graph Transformation Two graph reduction rules and an accepting graph for cyclic lists. Reduce: e e Finish: e e Acc: e Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19

19 Speeding up GP Dynamic searchplan generation, similar to GrGEN s method. Implementing rooted graph programs as an optional feature. Exploiting multi-core processors (parallelism). Chris Bak (The University of York) Graph Programming:Tools and Techniques January 19, / 19