A Parallel Branch and Bound Algorithm for the Maximum Labelled Clique Problem

The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new branch-and-bound algorithm for the problem, and explain how it may be parallelised. We evaluate an implementation on a set of benchmark instances, and show that it is consistently faster than previously published results, sometimes by four or five orders of magnitude.Comment: Author-final version. Accepted to Optimization Letter

Exact Algorithms for Maximum Clique: a computational study

We investigate a number of recently reported exact algorithms for the maximum clique problem (MCQ, MCR, MCS, BBMC). The program code used is presented and critiqued showing how small changes in implementation can have a drastic effect on performance. The computational study demonstrates how problem features and hardware platforms influence algorithm behaviour. The minimum width order (smallest-last) is investigated, and MCS is broken into its consituent parts and we discover that one of these parts degrades performance. It is shown that the standard procedure used for rescaling published results is unsafe.Comment: 40 pages, 14 figures, 10 tables, 12 short java program listings, code afailable to download at http://www.dcs.gla.ac.uk/~pat/maxClique/distribution

Teak: A Novel Computational And Gui Software Pipeline For Reconstructing Biological Networks, Detecting Activated Biological Subnetworks, And Querying Biological Networks.

As high-throughput gene expression data becomes cheaper and cheaper, researchers are faced with a deluge of data from which biological insights need to be extracted and mined since the rate of data accumulation far exceeds the rate of data analysis. There is a need for computational frameworks to bridge the gap and assist researchers in their tasks. The Topology Enrichment Analysis frameworK (TEAK) is an open source GUI and software pipeline that seeks to be one of many tools that fills in this gap and consists of three major modules. The first module, the Gene Set Cultural Algorithm, de novo infers biological networks from gene sets using the KEGG pathways as prior knowledge. The second and third modules query against the KEGG pathways using molecular profiling data and query graphs, respectively. In particular, the second module, also called TEAK, is a network partitioning module that partitions the KEGG pathways into both linear and nonlinear subpathways. In conjunction with molecular profiling data, the subpathways are ranked and displayed to the user within the TEAK GUI. Using a public microarray yeast data set, previously unreported fitness defects for dpl1 delta and lag1 delta mutants under conditions of nitrogen limitation were found using TEAK. Finally, the third module, the Query Structure Enrichment Analysis framework, is a network query module that allows researchers to query their biological hypotheses in the form of Directed Acyclic Graphs against the KEGG pathways

Threshold selection in gene co-expression networks using spectral graph theory techniques

Abstract Background Gene co-expression networks are often constructed by computing some measure of similarity between expression levels of gene transcripts and subsequently applying a high-pass filter to remove all but the most likely biologically-significant relationships. The selection of this expression threshold necessarily has a significant effect on any conclusions derived from the resulting network. Many approaches have been taken to choose an appropriate threshold, among them computing levels of statistical significance, accepting only the top one percent of relationships, and selecting an arbitrary expression cutoff. Results We apply spectral graph theory methods to develop a systematic method for threshold selection. Eigenvalues and eigenvectors are computed for a transformation of the adjacency matrix of the network constructed at various threshold values. From these, we use a basic spectral clustering method to examine the set of gene-gene relationships and select a threshold dependent upon the community structure of the data. This approach is applied to two well-studied microarray data sets from Homo sapiens and Saccharomyces cerevisiae. Conclusion This method presents a systematic, data-based alternative to using more artificial cutoff values and results in a more conservative approach to threshold selection than some other popular techniques such as retaining only statistically-significant relationships or setting a cutoff to include a percentage of the highest correlations

The Laplacian Paradigm in Deterministic Congested Clique

In this paper, we bring the techniques of the Laplacian paradigm to the congested clique, while further restricting ourselves to deterministic algorithms. In particular, we show how to solve a Laplacian system up to precision $\epsilon$ in $n^{o(1)}\log(1/\epsilon)$ rounds. We show how to leverage this result within existing interior point methods for solving flow problems. We obtain an $m^{3/7+o(1)}U^{1/7}$ round algorithm for maximum flow on a weighted directed graph with maximum weight $U$, and we obtain an $\tilde{O}(m^{3/7}(n^{0.158}+n^{o(1)}\text{poly}\log W))$ round algorithm for unit capacity minimum cost flow on a directed graph with maximum cost $W$. Hereto, we give a novel routine for computing Eulerian orientations in $O(\log n \log^* n)$ rounds, which we believe may be of separate interest.Comment: To be presented at the 42nd ACM Symposium on Principles of Distributed Computing (PODC 2023) as brief announcemen