2,395 research outputs found
Transcriptomic Data Analysis Using Graph-Based Out-of-Core Methods
Biological data derived from high-throughput microarrays can be transformed into finite, simple, undirected graphs and analyzed using tools first introduced by the Langston Lab at the University of Tennessee. Transforming raw data can be broken down into three main tasks: data normalization, generation of similarity metrics, and threshold selection. The choice of methods used in each of these steps effect the final outcome of the graph, with respect to size, density, and structure. A number of different algorithms are examined and analyzed to illustrate the magnitude of the effects.
Graph-based tools are then used to extract putative gene networks. These tools are loosely based on the concept of clique, which generates clusters optimized for density. Innovative additions to the paraclique algorithm, developed at the Langston Lab, are introduced to generate results that have highest average correlation or highest density. A new suite of algorithms is then presented that exploits the use of a priori gene interactions. Aptly named the anchored analysis toolkit, these algorithms use known interactions as anchor points for generating subgraphs, which are then analyzed for their graph structure. This results in clusters that might have otherwise been lost in noise.
A main product of this thesis is a novel collection of algorithms to generate exact solutions to the maximum clique problem for graphs that are too large to fit within core memory. No other algorithms are currently known that produce exact solutions to this problem for extremely large graphs. A combination of in-core and out-of-core techniques is used in conjunction with a distributed-memory programming model. These algorithms take into consideration such pitfalls as external disk I/O and hardware failure and recovery.
Finally, a web-based tool is described that provides researchers access the aforementioned algorithms. The Graph Algorithms Pipeline for Pathway Analysis tool, GrAPPA, was previously developed by the Langston Lab and provides the software needed to take raw microarray data as input and preprocess, analyze, and post-process it in a single package. GrAPPA also provides access to high-performance computing resources, via the TeraGrid
Multi-threading a state-of-the-art maximum clique algorithm
We present a threaded parallel adaptation of a state-of-the-art maximum clique
algorithm for dense, computationally challenging graphs. We show that near-linear speedups
are achievable in practice and that superlinear speedups are common. We include results for
several previously unsolved benchmark problems
Fine-grained Search Space Classification for Hard Enumeration Variants of Subset Problems
We propose a simple, powerful, and flexible machine learning framework for
(i) reducing the search space of computationally difficult enumeration variants
of subset problems and (ii) augmenting existing state-of-the-art solvers with
informative cues arising from the input distribution. We instantiate our
framework for the problem of listing all maximum cliques in a graph, a central
problem in network analysis, data mining, and computational biology. We
demonstrate the practicality of our approach on real-world networks with
millions of vertices and edges by not only retaining all optimal solutions, but
also aggressively pruning the input instance size resulting in several fold
speedups of state-of-the-art algorithms. Finally, we explore the limits of
scalability and robustness of our proposed framework, suggesting that
supervised learning is viable for tackling NP-hard problems in practice.Comment: AAAI 201
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
JGraphT -- A Java library for graph data structures and algorithms
Mathematical software and graph-theoretical algorithmic packages to
efficiently model, analyze and query graphs are crucial in an era where
large-scale spatial, societal and economic network data are abundantly
available. One such package is JGraphT, a programming library which contains
very efficient and generic graph data-structures along with a large collection
of state-of-the-art algorithms. The library is written in Java with stability,
interoperability and performance in mind. A distinctive feature of this library
is the ability to model vertices and edges as arbitrary objects, thereby
permitting natural representations of many common networks including
transportation, social and biological networks. Besides classic graph
algorithms such as shortest-paths and spanning-tree algorithms, the library
contains numerous advanced algorithms: graph and subgraph isomorphism; matching
and flow problems; approximation algorithms for NP-hard problems such as
independent set and TSP; and several more exotic algorithms such as Berge graph
detection. Due to its versatility and generic design, JGraphT is currently used
in large-scale commercial, non-commercial and academic research projects. In
this work we describe in detail the design and underlying structure of the
library, and discuss its most important features and algorithms. A
computational study is conducted to evaluate the performance of JGraphT versus
a number of similar libraries. Experiments on a large number of graphs over a
variety of popular algorithms show that JGraphT is highly competitive with
other established libraries such as NetworkX or the BGL.Comment: Major Revisio
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Zero-one IP problems: Polyhedral descriptions & cutting plane procedures
A systematic way for tightening an IP formulation is by employing classes of linear inequalities that define facets of the convex hull of the feasible integer points of the respective problems. Describing as well as identifying these inequalities will help in the efficiency of the LP-based cutting plane methods. In this report, we review classes of inequalities that partially described zero-one poly topes such as the 0-1 knapsack polytope, the set packing polytope and the travelling salesman polytope. Facets or valid inequalities derived from the 0-1 knapsack and the set packing polytopes are algorithmically identifie
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