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Yayın Colored simultaneous geometric embeddings(Springer-Verlag Berlin, 2007) Brandes, Ulrik; Erten, Cesim; Fowler, J. Joseph; Frati, Fabrizio; Geyer, Markus; Gutwenger, Carsten; Hong, Seok-Hee; Kaufmann, Michael; Kobourov, Stephen G.; Liotta, Giuseppe; Mutzel, Petra; Symvonis, AntoniosWe introduce the concept of colored simultaneous geometric embeddings as a generalization of simultaneous graph embeddings with and without mapping. We show that there exists a universal pointset of size n for paths colored with two or three colors. We use these results to show that colored simultaneous geometric embeddings exist for: (1) a 2-colored tree together with any number of 2-colored paths and (2) a 2-colored outerplanar graph together with any number of 2-colored paths. We also show that there does not exist a universal pointset of size n for paths colored with five colors. We finally show that the following simultaneous embeddings are not possible: (1) three 6-colored cycles, (2) four 6-colored paths, and (3) three 9-colored paths.Yayın Biclustering expression data based on expanding localized substructures(Springer-Verlag Berlin Heidelberg, 2009) Erten, Cesim; Sözdinler, MelihBiclustering gene expression data is the problem of extracting submatrices of genes and conditions exhibiting significant correlation across both the rows and the columns of a data matrix of expression values. We provide a method, LEB (Localize-and-Extract Biclusters) which reduces the search space into local neighborhoods within the matrix by first localizing correlated structures. The localization procedure takes its roots from effective use of graph-theoretical methods applied to problems exhibiting a similar structure to that of biclustering. Once interesting structures are localized the search space reduces to small neighborhoods and the biclusters are extracted from these localities. We evaluate the effectiveness of our method with extensive experiments both using artificial and real datasets.Yayın A robust biclustering method based on crossing minimization in bipartite graphs(Springer-Verlag Berlin, 2009) Erten, Cesim; Sözdinler, Melih[No abstract available]Yayın Fully decentralized, collaborative multilateration primitives for uniquely localizing WSNs(Springer-Verlag Berlin, 2009) Çakıroğlu, Olca Arda; Erten, CesimWe provide primitives for uniquely localizing WSN nodes. The goal is to maximize the number of uniquely localized nodes assuming a fully decentralized model of computation. Each node constructs a cluster of its own and applies unique localization primitives on it. These primitives are based on constructing a special order for multilaterating the nodes within the cluster. The proposed primitives are fully collaborative and thus the number of iterations required to compute the localization is fewer than that of the conventional iterative multilateration approaches. This further limits the messaging requirements. With relatively small clusters and iteration counts we can localize almost all the uniquely localizable nodes.Yayın Crossing minimization in weighted bipartite graphs(Springer, 2007) Çakıroğlu, Olca Arda; Erten, Cesim; Karataş, Ömer; Sözdinler, MelihGiven a bipartite graph G = (L-0, L-1, E) and a fixed ordering of the nodes in L-0, the problem of finding an ordering of the nodes in L-1 that minimizes the number of crossings has received much attention in literature. The problem is NP-complete in general and several practically efficient heuristics and polynomial-time algorithms with a constant approximation ratio have been suggested. We generalize the problem and consider the version where the edges have nonnegative weights. Although this problem is more general and finds specific applications in automatic graph layout problems similar to those of the unweighted case, it has not received as much attention. We provide a new technique that efficiently approximates a solution to this more general problem within a constant approximation ratio of 3. In addition we provide appropriate generalizations of some common heuristics usually employed for the unweighted case and compare their performances.
