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Liazi I Milis F Pascual and V Zissimopoulos Department of Informatics and Telecommunications University of Athens 157 84 Athens Greece mliazivassilis diuoagr Department of Informatics Athens University Economics and Business 104 34 Athens Greece. 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 Chen Rudolf Fleischer and Jian Li University of Notre Dame IN USA Email dchencsendedu Fudan University SCS and IIPL Shanghai China Email rudolffudaneducn University of Maryland College Park MD USA Email lijiancsumdedu Abstract We study approxi to maximum . clique graph. By,. Usha Kavirayani. OUTLINE. Problem . statement. Intersection Graphs of Boxes. Problem Solution. Graph . Construction. Maximum Clique. History. NP-Complete Graph. Techniques of dealing NP-Complete graphs. 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.. Degree 10 0 10 1 10 2 10 3 10 4 10 5 10 0 10 2 10 4 10 6 Total Subgraph 1 Subgraph 2 Subgraph 3 Degree 10 0 10 1 10 2 10 3 10 4 10 5 Count of Degree 10 0 10 2 10 4 10 6 Total Subgraph 1 Subgraph 2 Sub Admin. Last assignment out today (yay!). Review topics?. E-mail me if you have others…. CS senior theses . Wed 12:30-1:30 (MBH 538). Thur. 3-4:30 (MBH 104). Run-time analysis. We’ve spent a lot of . Subgroups. Chapter 7. Feb 20, 2009. Definition of subgroups . Definition of sub-groups: “Cohesive subgroups are subsets of actors among whom there are relatively strong, direct, intense, frequent or positive ties. It formalizes the strong social groups based on the social network properties ”. of Large Datasets. . Charalampos (Babis) E. Tsourakakis. Brown University. charalampos_tsourakakis@brown.edu. Brown University. Instructor. Neelima. Gupta. ngupta@. cs.du.ac.in. Presentation Edited by . Sapna. Grover. Table of Contents. NP – Hardness. Reductions. NP - . Hard. The aim to study this class is not to solve a problem but to see how hard . Distributions from Sampled Network Data. Minas . Gjoka. , Emily Smith, Carter T. Butts. University of California, Irvine. Outline. Problem statement. Estimation methodology. Results with real-life graphs. Extracting Optimal Quasi-Cliques with Quality . Guarantees. . Charalampos (Babis) E. Tsourakakis. charalampos.tsourakakis@aalto.fi. KDD 2013. Given a set of real numbers, output a sequence, . (. l. 1. , … , . l. i. , … , . l. n. ). , . where . l. i. . ≤ . l. i 1. . for . i. = . 1 … n-1 .. Naive Algorithm. For index . i. =1 .. . (CPM). What is CPM?. Algorithm. Analysis. Conclusion. Contents. Method to find . overlapping. . communities. Based on concept:. internal edges of community likely to form cliques. Intercommunity edges unlikely to form cliques.