1. Research Directions for Big Data Graph Analytics John A. Miller, Lakshmish Ramaswamy, Krys J. Kochut and Arash Fard

2. Contents  Introduction  What is Graph Analytics?  Problems in Graph Analytics  Path Problems  Pattern Problems  Pattern Matching Models  Applications  Computational Models & Frameworks  Conclusion

3. What,Why and Where ?  Large Data Graphs, query processing and Iterative algorithms.  Big Data Graph Analytics  Wide Ranging Domain Page Rank Algorithm, Relationship Analysis, Maps and Bio-chemistry.  Traditional graph computation algorithms.  Scalable graph analytics is still a challenge designing algorithms, performance, indexing, geographic distribution

4. Graph Analytics  data items :labeled vertices, & relationships : labeled edges  Labelled Multi-Digraphs - Vertex labeled Digraphs - directed graph with edge labels - Fully labelled Multi-Digraph - adds edge labels - allows multiple edges between 2 vertices if labels are distinct - G(V, E, L, l) : vertices, labeled edges, label set, vertex labeling

5. Problems in Graph Analytics  Problems can broadly classified in three categories  Path Problems – Reachability – Shortest Path  Pattern Problems – Graph Simulation – Graph Morphisms  Partition Problems

6. Path Problems  Reachability – Given a graph G and two vertices, u, w ∈ G.V, – find a path (sequence of edges) connecting them path(u, w) = uv 1 l i1, v 1 v 2 l i2,..., v n w l in+1 ∈ G.E – Reachability is simply reach(u, w) = path(u, w)  Shortest Path – Given k vertices, find a minimum distance path that – includes all k vertices. – Algorithms: Dijkstra, Bellman-Ford

7. Pattern Problems  Pattern Matching Model – Given a query graph Q, match its labeled vertices to corresponding labeled vertices in a data graph G Φ : Q.V → 2 G.V – All the pattern matching models start with matching vertex labels – For each vertex u in Q.V, require ∀ u' ∈ Φ (u), l(u') = l(u)  Graph Simulation – For each label matching pair (u, u') in Q.V × G.V, – require matching children ∀ v ∈ child Q (u), v' ∈ Φ (v) ∃ such that u’ v' ∈ G.E

8. Pattern Problems  Dual Simulation – For each vertex pair (u, u') in Q.V × G.V, also require matching parents ∀ w ∈ parent Q (u), w’ ∈ Φ (w) ∃ such that w’ u' ∈ G.E  Strong Simulation – Matching patterns in G must be contained in some ball B radius(B) = diameter(Q)

9. Pattern Problems  Strict Simulation – only balls containing vertices in an initial dual match  Tight Simulation – only balls with centers corresponding to a central vertex in Q radius(B) = diameter(Q)  CAR-tight Simulation – child and parent match must satisfy

10. Pattern Problems  Graph Homomorphism – Mapping function f: Q.V → G.V such that ∀ u ∈ Q, u' = f(u), l(u') = l(u) u v ∈ Q.E implies u'v’ ∈ G.E  Sub-graph Isomorphism - If we further require the mapping functions to be bijections between Q.V and G’.V, where G’ is a sub-graph of G (G’ ⊆ G) Difference : correspondence between vertices, one-to-one correspondence

11. Applications  Graph Databases – Neo4j, Orient DB and Titan  Semantic Web – SPARQL Queries – (subject, predicate, object) subject -edge-> object e.g. SELECT ?x, ?y, ?z WHERE { x a Lawyer. y a Doctor. z a Lawyer. x friend y. x competes_with z. y friend z }  Social Media - Facebook, Twitter, LinkedIn, Amazon

12. Computational Models & Frameworks  MapReduce/Hadoop  Apache Storm  Apache Spark  Bulk Synchronous Parallel (BSP) - BSP can be quite useful for implementing graph algorithms - vertex-centric, has become popular for big data graph analytics. - significant overhead in the synchronization

13. Conclusion  Graphs are now becoming an important form of representation for data.  Implementation of improved sequential algorithms  Adding of Extensions.

14. Questions ??