PPT-On the Clique vs Independent Set Problem

The Clique vs IndependentSet Problem Yannakakis 88 CIS G Publicly known G VE Vn Alice Clique C µ V Bob Independent Set I µ V Goal . CHEPOI AND FEODOR F DRAGAN SIAM J D ISCRETE ATH 1997 Society for Industrial and Applied Mathematics Vol 10 No 1 pp 109127 February 1997 009 Abstract Let be a family of cliques of a graph VE Suppose that each clique of is associated with an integer Cliques, Quasi-Cliques and Clique Partitions in Graphs. Panos. M. Pardalos. Notations. is a simple undirected graph with vertex set and . . is the . 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. Dr. Yingwu Zhu. Chapter 34. 2. NP-Completeness. Poly time algorithm: input size . n . (in some encoding), worst case running time – . O. (. n. c. ) for some constant . c. .. Three classes of problems. 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 . CS302, Spring 2013. David Kauchak. Admin. Last assignment out today (yay!). Review topics?. E-mail me if you have others…. CS senior theses. Tue 3-4, Wed 3-4:30, . Thur. 3-4 in MBH 104. NP problems. , Convexity, and the quest towards Optimal Algorithms. Boaz Barak. Harvard University. Microsoft Research. Partially based on work in progress with . Sam Hopkins. , . Jon Kelner, . Pravesh Kothari. , Ankur Moitra and Aaron Potechin.. Cliques, Quasi-Cliques and Clique Partitions in Graphs. Panos. M. Pardalos. Notations. is a simple undirected graph with vertex set and . . is the . Algorithms. and Networks 2016/2017. Johan M. M. van Rooij. Hans L. . Bodlaender. This lecture. Classical complexity: . P. . vs. . NP. .. Conditional non-existence proofs.. Parameterised complexity:. 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. Jeffrey . Pattillo. , . Nataly. . Youssef. , and . Sergiy. . Butenko. Suchitra. . Ganga. . Bhavani. . Anusha. . Inti. 810846173. Social networks represent certain types of social interaction, such as . 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.