Cesim Erten

SPINAL: Scalable Protein Interaction Network Alignment

MOTIVATION Given protein-protein interaction (PPI) networks of a pair of species, a pairwise global alignment corresponds to a one-to-one mapping between their proteins. Based on the presupposition that such a mapping provides pairs of functionally orthologous proteins accurately, the results of the alignment may then be used in comparative systems biology problems such as function prediction/verification or construction of evolutionary relationships. RESULTS We show that the problem is NP-hard even for the case where the pair of networks are simply paths. We next provide a polynomial time heuristic algorithm, SPINAL, which consists of two main phases. In the first coarse-grained alignment phase, we construct all pairwise initial similarity scores based on pairwise local neighborhood matchings. Using the produced similarity scores, the fine-grained alignment phase produces the final one-to-one mapping by iteratively growing a locally improved solution subset. Both phases make use of the construction of neighborhood bipartite graphs and the contributors as a common primitive. We assess the performance of our algorithm on the PPI networks of yeast, fly, human and worm. We show that based on the accuracy measures used in relevant work, our method outperforms the state-of-the-art algorithms. Furthermore, our algorithm does not suffer from scalability issues, as such accurate results are achieved in reasonable running times as compared with the benchmark algorithms. AVAILABILITY Supplementary Document, open source codes, useful scripts, all the experimental data and the results are freely available at http://code.google.com/p/spinal/. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

Simultaneous Graph Drawing: Layout Algorithms and Visualization Schemes

In this paper we consider the problem of drawing and displaying a series of related graphs, i.e., graphs that share all, or parts of the same vertex set. We designed and implemented three different algorithms for simultaneous graph drawing and three different visualization schemes. The algorithms are based on a modification of the force-directed algorithm that allows us to take into account vertex weights and edge weights in order to achieve mental map preservation while obtaining individually readable drawings. The implementation is in Java and the system can be downloaded at http://simg.cs.arizona.edu/.

Force-directed approaches to sensor localization

As 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 sensors 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.

BEAMS: Backbone Extraction and Merge Strategy for the Global Many-to-Many Alignment of Multiple PPI Networks

MOTIVATION Global many-to-many alignment of biological networks has been a central problem in comparative biological network studies. Given a set of biological interaction networks, the informal goal is to group together related nodes. For the case of protein-protein interaction networks, such groups are expected to form clusters of functionally orthologous proteins. Construction of such clusters for networks from different species may prove useful in determining evolutionary relationships, in predicting the functions of proteins with unknown functions and in verifying those with estimated functions. RESULTS A central informal objective in constructing clusters of orthologous proteins is to guarantee that each cluster is composed of members with high homological similarity, usually determined via sequence similarities, and that the interactions of the proteins involved in the same cluster are conserved across the input networks. We provide a formal definition of the global many-to-many alignment of multiple protein-protein interaction networks that captures this informal objective. We show the computational intractability of the suggested definition. We provide a heuristic method based on backbone extraction and merge strategy (BEAMS) for the problem. We finally show, through experiments based on biological significance tests, that the proposed BEAMS algorithm performs better than the state-of-the-art approaches. Furthermore, the computational burden of the BEAMS algorithm in terms of execution speed and memory requirements is more reasonable than the competing algorithms. AVAILABILITY AND IMPLEMENTATION Supplementary material including code implementations in LEDA C++, experimental data and the results are available at http://webprs.khas.edu.tr/~cesim/BEAMS.tar.gz.

Simultaneous Embedding of a Planar Graph and Its Dual on the Grid

Abstract Traditional representations of graphs and their duals suggest that the dual vertices should be placed inside their corresponding primal faces, and the edges of the dual graph should only cross their corresponding primal edges. We consider the problem of simultaneously embedding a planar graph and its dual on a small integer grid such that the edges are drawn as straight-line segments and the only crossings are between primal--dual pairs of edges. We provide an O(n) time algorithm that simultaneously embeds a 3-connected planar graph and its dual on a (2n - 2) × (2n - 2) integer grid, where n is the total number of vertices in the graph and its dual. All the edges are drawn as straight-line segments except for one edge on the outer face, which is drawn using two segments.

On Simultaneous Planar Graph Embeddings

We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another in which the mapping is not given. In particular, given a mapping, we show how to embed two paths on an n ×n grid, and two caterpillar graphs on a 3n ×3n grid. We show that it is not always possible to simultaneously embed three paths. If the mapping is not given, we show that any number of outerplanar graphs can be embedded simultaneously on an O(n) ×O(n) grid, and an outerplanar and general planar graph can be embedded simultaneously on an O(n 2) ×O(n 2) grid.

Intersection-Free Morphing of Planar Graphs

Given two different drawings of a planar graph we consider the problem of morphing one drawing into the other. We designed and implemented an algorithm for intersection-free morphing of planar graphs. Our algorithm uses a combination of different techniques to achieve smooth transformations: rigid morphing, compatible triangulations, as well as morphing based on interpolation of the convex representations of the graphs. Our algorithm can morph between drawings with straight-line segments, bends, and curves. Our system is implemented in Java and available as an applet at http://gmorph.cs.arizona.edu.

Colored simultaneous geometric embeddings

We 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.

Exploring the computing literature using temporal graph visualization

We present a system for the visualization of computing literature with an emphasis on collaboration patterns, interactions between related research specialties and the evolution of these characteristics through time. Our computing literature visualization system, has four major components: A mapping of bibliographical data to relational schema coupled with an RDBMS to store the relational data, an interactive GUI that allows queries and the dynamic construction of graphs, a temporal graph layout algorithm, and an interactive visualization tool. We use a novel technique for visualization of large graphs that evolve through time. Given a dynamic graph, the layout algorithm produces two-dimensional representations of each timeslice, while preserving the mental map of the graph from one slice to the next. A combined view, with all the timeslices can also be viewed and explored. For our analysis we use data from the Association of Computing Machinerys Digital Library of Scientific Literature which contains more than one hundred thousand research papers and authors. Our system can be found online at http://tgrip.cs.arizona.edu.

Morphing planar graphs

We describe an efficient algorithm and implementation for morphing planar graphs. The algorithm generalizes the notion of compatible triangulations of polygons to compatible triangulations of planar graphs and applies a combination of affine transformation morph and barycentric-representation morph to find smooth and crossing-free transformations between different drawings of a given planar graph. The video presentation and our Java applet can be found at http: //gmorph.cs.arizona.edu. Morphing refers to the process of transforming one shape (the source) into another (the target). Morphing is widely used in graph drawing, computer graphics, animation, and modeling [2, 3, 4]. In planar graph morphing we would like to transform a given source graph to another pre-specified target graph. Smooth transformation of one graph into another is useful for numerous graph drawing problems. In particular, when dealing with dynamic graphs and graphs that change through time, it is important to preserve the mental map of the user. Thus, it is important to minimize the changes to the drawing and to create a smooth transition between consecutive drawings. We consider the problem of morphing between two drawings, Ds and Dt, of the same planar graph G = (V, E). We assume that both drawings are crossing-free and realize the same embedding of G (otherwise, a crossing-free morph does not exist). The source drawing Ds and the target drawing Dt can be straight-line drawings, or drawings with bends and curves. The main objective is to find a morph that does not introduce crossings in the intermediate drawings throughout the transformation. Secondary objectives include obtaining simple and smooth trajectories for the vertices (and bends) and preserving drawing invariants throughout the transformation.