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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 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 Colored simultaneous geometric embeddings and universal pointsets(Springer, 2011-07) Brandes, Ulrik; Erten, Cesim; Estrella-Balderrama, Alejandro; Fowler, J. Joseph; Frati, Fabrizio; Geyer, Markus; Gutwenger, Carsten; Hong, Seok-Hee; Kaufmann, Michael; Kobourov, Stephen G.; Liotta, Giuseppe; Mutzel, Petra; Symvonis, AntoniosUniversal pointsets can be used for visualizing multiple relationships on the same set of objects or for visualizing dynamic graph processes. In simultaneous geometric embeddings, the same point in the plane is used to represent the same object as a way to preserve the viewer's mental map. In colored simultaneous embeddings this restriction is relaxed, by allowing a given object to map to a subset of points in the plane. Specifically, consider a set of graphs on the same set of n vertices partitioned into k colors. Finding a corresponding set of k-colored points in the plane such that each vertex is mapped to a point of the same color so as to allow a straight-line plane drawing of each graph is the problem of colored simultaneous geometric embedding. For n-vertex paths, we show that there exist universal pointsets of size n, colored with two or three colors. We use this result to construct colored simultaneous geometric embeddings for a 2-colored tree together with any number of 2-colored paths, and more generally, a 2-colored outerplanar graph together with any number of 2-colored paths. For n-vertex trees, we construct small near-universal pointsets for 3-colored caterpillars of size n, 3-colored radius-2 stars of size n+3, and 2-colored spiders of size n. For n-vertex outerplanar graphs, we show that these same universal pointsets also suffice for 3-colored K (3)-caterpillars, 3-colored K (3)-stars, and 2-colored fans, respectively. We also present several negative results, showing that there exist a 2-colored planar graph and pseudo-forest, three 3-colored outerplanar graphs, four 4-colored pseudo-forests, three 5-colored pseudo-forests, five 5-colored paths, two 6-colored biconnected outerplanar graphs, three 6-colored cycles, four 6-colored paths, and three 9-colored paths that cannot be simultaneously embedded.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.Yayın Crossing minimization in weighted bipartite graphs(Elsevier B.V., 2009-12) Çakıroğlu, Olca Arda; Erten, Cesim; Karataş, Ömer; Sözdinler, MelihGiven a bipartite graph G = (L0, L1, E) and a fixed ordering of the nodes in L0, the problem of finding an ordering of the nodes in L1 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.Yayın Force-directed approaches to sensor localization(SIAM, 2006) Efrat, Alon; Forrester, David; Iyer, Anand; Kobourov, Stephen G.; Erten, CesimWe consider the centralized, anchor-free sensor localization problem. We consider the case where the sensor network reports range information and the case where in addition to the range, we also have angular information about the relative order of each sensor's neighbors. We experimented with classic and new force-directed techniques. The classic techniques work well for small networks with nodes distributed in simple regions. However, these techniques do not scale well with network size and yield poor results with noisy data. We describe a new force-directed technique, based on a multi-scale dead-reckoning, that scales well for large networks, is resilient under range errors, and can reconstruct complex underlying regions.Yayın Force-directed approaches to sensor localization(Assoc Computing Machinery, 2010-09) Efrat, Alon; Forrester, David; Iyer, Anand; Kobourov, Stephen G.; Erten, Cesim; Kılıç, Yasin OzanAs the number of applications of sensor networks increases, so does the interest in sensor network localization, that is, in recovering the correct position of each node in a network of sensors from partial connectivity information such as adjacency, range, or angle between neighboring nodes. In this article, we consider the anchor-free localization problem in sensor networks that report possibly noisy range information and angular information about the relative order of each sensor's neighbors. Previously proposed techniques seem to successfully reconstruct the original positions of the nodes for relatively small networks with nodes distributed in simple regions. However, these techniques do not scale well with network size and yield poor results with nonconvex or nonsimple underlying topology. Moreover, the distributed nature of the problem makes some of the centralized techniques inapplicable in distributed settings. To address these problems we describe a multiscale dead-reckoning (MSDR) algorithm that scales well for large networks, can reconstruct complex underlying topologies, and is resilient to noise. The MSDR algorithm takes its roots from classic force-directed graph layout computation techniques. These techniques are augmented with a multiscale extension to handle the scalability issue and with a dead-reckoning extension to overcome the problems arising with nonsimple topologies. Furthermore, we show that the distributed version of the MSDR algorithm performs as well as, if not better than, its centralized counterpart, as shown by the quality of the layout, measured in terms of the accuracy of the computed pairwise distances between sensors in the network.Yayın Fully decentralized and collaborative multilateration primitives for uniquely localizing WSNs(Springer International Publishing AG, 2010) 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 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 GSPIM: Graphical visualization tool for MIPS assembly programming and simulation(2007) Borunda, Patrick; Brewer, Chris; Erten, CesimWe describe our system, GSPIM, used for visualization of low-level MIPS Assembly programming and simulation. Although many visualization tools for algorithms and high-level programs have been considered in educational settings, visualization specific to low-level programs have not received enough consideration. One desirable property of such a visualization is that it should close the gap between high-level programming constructs and the sequential nature of low-level programs. Secondly it should provide techniques to present information specific to the simulation of the code. GSPIM supports both properties and is publicly available at http://www.cs.arizona.edu/~cesim/ gspim.tar.gz.Yayın A robust biclustering method based on crossing minimization in bipartite graphs(Springer-Verlag Berlin, 2009) Erten, Cesim; Sözdinler, Melih[No abstract available]Yayın A robust localization framework to handle noisy measurements in wireless sensor networks(IEEE, 2009-09-14) Erten, Cesim; Karataş, ÖmerWe construct a robust localization framework to handle noisy measurements in wireless sensor networks. Traditionally many approaches employ the distance information gathered from ranging devices of the sensor nodes to achieve localization. However the measurements of these devices may contain noise both as hardware noise and as environmental noise due to the employment conditions of the network. It Is necessary to provide a general framework that handles such a noise in data and yet still be applicable within several localization algorithms. In order to handle noise in distance measurements, our framework utilizes convex constraints and confidence intervals of a random variable. At the end of the localization process nodes are assigned to a set of feasible regions with corresponding probabilities. The accuracy of the localization can be adjusted and the framework can easily be embedded to work within previously suggested localization algorithms.
