PDF-The K clique Densest Subgraph Problem

10 HoweverfrequentlythedensestsubgraphproblemfailsindetectinglargenearcliquesinnetworksInthisworkweintroducethecliquedensestsubgraphproblem2Thisgeneralizesthewellstudieddensestsubgraphprobl. 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 Tsourakakis Francesco Bonchi Aristides Gionis Francesco Gullo Maria A Tsiarli Carnegie Mellon University Yahoo Research Aalto University University of Pittsburgh Pittsburgh PA USA Barcelona Spain Espoo Finland Pittsbu rgh PA USA ABSTRACT Finding den edu Ravi Kumar Yahoo Research Sunnyvale CA ravikumaryahooinccom Sergei Vassilvitskii Yahoo Research New York NY sergeiyahooinccom ABSTRACT The problem of nding locally dense components of a graph is an important primitive in data analysis with widera Both results are of similar avor ruling out constant factor approximations in polynomial time for the D S problem under an average case hardness assumption The rst result asserts that if Random AND formulas are hard to distinguish from ones that are 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 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 Extracting Optimal Quasi-Cliques with Quality . Guarantees. . Charalampos (Babis) E. Tsourakakis. charalampos.tsourakakis@aalto.fi. KDD 2013. of Large Datasets. . Charalampos (Babis) E. Tsourakakis. Brown University. charalampos_tsourakakis@brown.edu. Brown University. and. Core-periphery . structure. By: Ralucca Gera, NPS. Why?. Mostly observed real networks have:. Heavy tail (. powerlaw. most probably, exponential). High clustering (high number of triangles especially in social networks, lower count otherwise). of Large Datasets. . Charalampos (Babis) E. Tsourakakis. Brown University. charalampos_tsourakakis@brown.edu. Brown University. Jeffrey . Pattillo. , . Nataly. . Youssef. , and . Sergiy. . Butenko. Suchitra. . Ganga. . Bhavani. . Anusha. . Inti. 810846173. Social networks represent certain types of social interaction, such as . Extracting Optimal Quasi-Cliques with Quality . Guarantees. . Charalampos (Babis) E. Tsourakakis. charalampos.tsourakakis@aalto.fi. KDD 2013. Subgraph. . with Perfect Completeness. Aviad Rubinstein (UC Berkeley). Mark . Braverman. , Young Kun . Ko. , and . Omri. Weinstein. A confession…. rest of workshop. this talk. vs . vs . SETH: SAT requires . 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 ”.