PPT-Graph Isomorphism Algorithms and networks

Graph Isomorphism 2 Today Graph isomorphism definition Complexity isomorphism completeness The refinement heuristic Isomorphism for trees Rooted trees Unrooted trees Graph Isomorphism 3 Graph Isomorphism. Sometimes, two graphs have exactly the same form, in the sense that there is a one-to-one correspondence between their vertex sets that preserves edges. In such a case, we say that the two graphs are . 1. Graph Algorithms. Many problems are naturally represented as graphs. Networks, Maps, Possible paths, Resource Flow, etc.. Ch. 3 focuses on algorithms to find connectivity in graphs. Ch. 4 focuses on algorithms to find paths within graphs. Lasserre. Gaps,. and Asymmetry of Random Graphs. Ryan O’Donnell (CMU). John Wright (CMU). Chenggang. Wu (. Tsinghua. ). Yuan Zhou (CMU). Hardness of . Robust Graph Isomorphism. ,. . Lasserre. Gaps,. Using the Ullman Algorithm for Graphical Matching. Iddo. . Aviram. OCR- a Brief Review. Optical character recognition. , usually abbreviated to . OCR. , is the mechanical or electronic translation of scanned images of handwritten, typewritten or printed text into machine-encoded text. George Caragea, and Uzi Vishkin. University of Maryland. 1. Speaker. James Edwards. It has proven to be quite . difficult. to obtain significant performance improvements using current parallel computing platforms.. in Dynamic Graphs. Viswanath. . Gunturi. (4192285). Bala. . Subrahmanyam. . Kambala. (4451379) . Application Domain. Transportation Networks:. Sample Dataset. Sample dataset showing the dynamic nature . Sometimes, two graphs have exactly the same form, in the sense that there is a one-to-one correspondence between their vertex sets that preserves edges. In such a case, we say that the two graphs are . Lasserre. Gaps,. and Asymmetry of Random Graphs. Ryan O’Donnell (CMU). John Wright (CMU). Chenggang. Wu (. Tsinghua. ). Yuan Zhou (CMU). Hardness of . Robust Graph Isomorphism. ,. . Lasserre. Gaps,. Section . 10.3. Representing Graphs: . Adjacency Lists. Definition. : An . adjacency list . can be used to represent a graph with no multiple edges by specifying the vertices that are adjacent to each vertex of the graph.. (and related problems). on Minor-Free Graphs. Hans . Bodlaender. (U Utrecht, TU Eindhoven). Jesper. . Nederlof. (TU Eindhoven). Tom van der . Zanden. (U Utrecht). 1. Subgraph Isomorphism. Given: a . CIS 606. Spring 2010. Graph representation. Given graph . G. . = (. V. , . E. ). . In . pseudocode. , represent vertex set by . G.V . and edge . set by . G.E. .. G . may be either directed or undirected.. Matching Algorithms and Networks Algorithms and Networks: Matching 2 This lecture Matching: problem statement and applications Bipartite matching (recap) Matching in arbitrary undirected graphs: Edmonds algorithm Lasserre. Gaps,. and Asymmetry of Random Graphs. Ryan O’Donnell (CMU). John Wright (CMU). Chenggang. Wu (. Tsinghua. ). Yuan Zhou (CMU). Hardness of . Robust Graph Isomorphism. ,. . Lasserre. Gaps,. . graph. . partitioning. . - . Dividing. . networks. . into. . clusters. - Graph . partitioning. - The . Kernighan. -Lin . algorithm. - . Spectral. . partitioning. 1. SS 2014 - . lecture. 3. Mathematics of Biological Networks.