PPT-Subexponential Algorithms for Subgraph Isomorphism

and related problems on MinorFree Graphs Hans Bodlaender U Utrecht TU Eindhoven Jesper Nederlof TU Eindhoven Tom van der Zanden U Utrecht 1 Subgraph Isomorphism Given a . There is a signi64257cant gap between the best known upper and lower bounds for this problem It is NPhard and does not have a PTAS unless NP has subexponential time algorithms On the other hand the current best known algorithm of Feige Kortsarz and R. ULLMANN Physical Laboratory, Tedd, ngton, M, ddlcsex, England Subgraph isomorphism can be determined by means of a brute-force tree-search enu- meration procedure. In this paper a new algorithm is 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,. Extracting Optimal Quasi-Cliques with Quality . Guarantees. . Charalampos (Babis) E. Tsourakakis. charalampos.tsourakakis@aalto.fi. KDD 2013. Longin Jan Latecki. Based on :. P. . Dupont. , J. . Callut. , G. Dooms, J.-N. . Monette. and Y. Deville.. Relevant subgraph extraction from random walks in a graph. . RR 2006-07, Catholic University of Louvain , November 2006.. 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. Arijit Khan, . Yinghui. Wu, Xifeng Yan. Department of Computer Science. University of California, Santa Barbara. {. arijitkhan. , . yinghui. , . xyan. }@. cs.ucsb.edu. Graph Data. 2. Graphs are everywhere.. Janine Bennett. 1. William . McLendon. III. 1. Guarav. Bansal. 2. Peer-. Timo. Bremer. 3. Jacqueline Chen. 1. Hemanth. Kolla. 1. 1. Sandia National Laboratories, . 2. Intel, . 3. Lawrence Livermore . Simple algorithms. Given two graphs G = (V,E) and H = (W,F). is there a subgraph of H that is isomorphic to G?. Given two graphs G = (V,E) and H = (W,F). is there a subgraph of H that is isomorphic to G?. 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,. Organization theory. Do . organizations always act similarly?. Agenda. Memo presentation #1 (. Hannan. & Freeman, 1977). Memo discussion #1. Memo presentation #2 (Hsu & . Hannan. , 2005). Memo discussion #2. 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. Longin Jan Latecki. Based on :. P. . Dupont. , J. . Callut. , G. Dooms, J.-N. . Monette. and Y. Deville.. Relevant subgraph extraction from random walks in a graph. . RR 2006-07, Catholic University of Louvain , November 2006.. 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,.