Algorithms for string and graph layout

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 121-125).Many graph optimization problems can be viewed as graph layout problems. A layout of a graph is a geometric arrangement of the vertices subject to given constraints. For example, the vertices of a graph can be arranged on a line or a circle, on a two- or three-dimensional lattice, etc. The goal is usually to place all the vertices so as to optimize some specified objective function. We develop combinatorial methods as well as models based on linear and semidefinite programming for graph layout problems. We apply these techniques to some well-known optimization problems. In particular, we give improved approximation algorithms for the string folding problem on the two- and three-dimensional square lattices. This combinatorial graph problem is motivated by the protein folding problem, which is central in computational biology. We then present a new semidefinite programming formulation for the linear ordering problem (also known as the maximum acyclic subgraph problem) and show that it provides an improved bound on the value of an optimal solution for random graphs. This is the first relaxation that improves on the trivial "all edges" bound for random graphs.by Alantha Newman.Ph.D

Online visualization of bibliography Using Visualization Techniques

Visualization is a concept where we can represent some raw data in the form of graphs, images, charts, etc. which will be very helpful for the end-user to correlate and be able to understand the relationships between the data elements in a single screen. Representing the bibliographic information of the computer science journals and proceedings using Visualization technique would help user choose a particular author and navigate through the hierarchy and find out what papers the author has published, the keywords of the papers, what papers cite them, the co-authors along with the main author, and how many papers are published by the author selected by the user and so on in a single page. These information is right now present in a scattered manner and the user has to search on websites like Google Scholar [1], Cite Seer [2] to get these bibliographic records. By the use of visualization techniques, all the information can be accessed on a single page by having a graph like points on the page, where the user can search for a particular author and the author and its co-authors are represented in the form of points. The goal of this project is to enhance current bibliography web services with an intuitive interactive visualization interface and to improve user understanding and conceptualization. In this project, we develop a simple web-interface which will take a search query from the user and find the related information like author\u27s name, the co-authors, number of papers published by him, related keywords, citations referred etc. The project uses the bibliographic records which are available as XML files from the Citeseer database[2], extracts the data into the database and then queries the database for the results using a web service. The data which is extracted is then presented visually to allow the user to conceptualize the results in a better way and help him/her find the articles of interest with utmost ease. In addition the user can interactively navigate the visual results to get more information about any of the article or the author displayed. So here we present both paper centric view and author centric view to the user by representing data in terms of graphs. The nodes in the graphs obtained for paper centric views and author centric views are color coded based on the paper’s weight parameter ( popularity of the paper ). For the paper centric view, the papers which are referring other papers are represented by providing a directed arrow from referred paper to referenced paper. Overall the idea here was to represent this related data in the form of a tree, so that the user can correlate all the data and get the relationships between them

Structure induction by lossless graph compression

This work is motivated by the necessity to automate the discovery of structure in vast and evergrowing collection of relational data commonly represented as graphs, for example genomic networks. A novel algorithm, dubbed Graphitour, for structure induction by lossless graph compression is presented and illustrated by a clear and broadly known case of nested structure in a DNA molecule. This work extends to graphs some well established approaches to grammatical inference previously applied only to strings. The bottom-up graph compression problem is related to the maximum cardinality (non-bipartite) maximum cardinality matching problem. The algorithm accepts a variety of graph types including directed graphs and graphs with labeled nodes and arcs. The resulting structure could be used for representation and classification of graphs.Comment: 10 pages, 7 figures, 2 tables published in Proceedings of the Data Compression Conference, 200

Simultaneous Embeddability of Two Partitions

We study the simultaneous embeddability of a pair of partitions of the same underlying set into disjoint blocks. Each element of the set is mapped to a point in the plane and each block of either of the two partitions is mapped to a region that contains exactly those points that belong to the elements in the block and that is bounded by a simple closed curve. We establish three main classes of simultaneous embeddability (weak, strong, and full embeddability) that differ by increasingly strict well-formedness conditions on how different block regions are allowed to intersect. We show that these simultaneous embeddability classes are closely related to different planarity concepts of hypergraphs. For each embeddability class we give a full characterization. We show that (i) every pair of partitions has a weak simultaneous embedding, (ii) it is NP-complete to decide the existence of a strong simultaneous embedding, and (iii) the existence of a full simultaneous embedding can be tested in linear time.Comment: 17 pages, 7 figures, extended version of a paper to appear at GD 201

Linear orderings of random geometric graphs (extended abstract)

In random geometric graphs, vertices are randomly distributed on [0,1]^2 and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study several layout problems on random geometric graphs: Bandwidth, Minimum Linear Arrangement, Minimum Cut, Minimum Sum Cut, Vertex Separation and Bisection. We first prove that some of these problems remain \NP-complete even for geometric graphs. Afterwards, we compute lower bounds that hold with high probability on random geometric graphs. Finally, we characterize the probabilistic behavior of the lexicographic ordering for our layout problems on the class of random geometric graphs.Postprint (published version

On Semantic Word Cloud Representation

We study the problem of computing semantic-preserving word clouds in which semantically related words are close to each other. While several heuristic approaches have been described in the literature, we formalize the underlying geometric algorithm problem: Word Rectangle Adjacency Contact (WRAC). In this model each word is associated with rectangle with fixed dimensions, and the goal is to represent semantically related words by ensuring that the two corresponding rectangles touch. We design and analyze efficient polynomial-time algorithms for some variants of the WRAC problem, show that several general variants are NP-hard, and describe a number of approximation algorithms. Finally, we experimentally demonstrate that our theoretically-sound algorithms outperform the early heuristics