Analysis and Enumeration
Algorithms for Biological Graphs
Authors: Marino, Andrea
 Provides the reader with a systematic description of the main techniques to design enumeration algorithms
 Fills a gap in the existing literature on enumeration algorithms in general and on biological enumeration algorithms especially
 Gives the reader a detailed insight in four new examples of enumeration algorithms
Buy this book
 About this book

In this work we plan to revise the main techniques for enumeration algorithms and to show four examples of enumeration algorithms that can be applied to efficiently deal with some biological problems modelled by using biological networks: enumerating central and peripheral nodes of a network, enumerating stories, enumerating paths or cycles, and enumerating bubbles. Notice that the corresponding computational problems we define are of more general interest and our results hold in the case of arbitrary graphs. Enumerating all the most and less central vertices in a network according to their eccentricity is an example of an enumeration problem whose solutions are polynomial and can be listed in polynomial time, very often in linear or almost linear time in practice. Enumerating stories, i.e. all maximal directed acyclic subgraphs of a graph G whose sources and targets belong to a predefined subset of the vertices, is on the other hand an example of an enumeration problem with an exponential number of solutions, that can be solved by using a non trivial bruteforce approach. Given a metabolic network, each individual story should explain how some interesting metabolites are derived from some others through a chain of reactions, by keeping all alternative pathways between sources and targets. Enumerating cycles or paths in an undirected graph, such as a proteinprotein interaction undirected network, is an example of an enumeration problem in which all the solutions can be listed through an optimal algorithm, i.e. the time required to list all the solutions is dominated by the time to read the graph plus the time required to print all of them. By extending this result to directed graphs, it would be possible to deal more efficiently with feedback loops and signed paths analysis in signed or interaction directed graphs, such as gene regulatory networks. Finally, enumerating mouths or bubbles with a source s in a directed graph, that is enumerating all the two vertexdisjoint directed paths between the source s and all the possible targets, is an example of an enumeration problem in which all the solutions can be listed through a linear delay algorithm, meaning that the delay between any two consecutive solutions is linear, by turning the problem into a constrained cycle enumeration problem. Such patterns, in a de Bruijn graph representation of the reads obtained by sequencing, are related to polymorphisms in DNA or RNAseq data.
 Reviews

“This book is the publication of author's Ph.D. dissertation [Algorithms for biological graphs: analysis and enumeration, Univ. Florence, 2013] and is supported by the Italian Chapter of the EATCS. Only two dissertations a year might get this recognition so, as one expects, this is a high level text. … The book itself is nice to read and has an excellent bibliography.” (András Sándor Pluhár, Mathematical Reviews, April, 2017)
 Download Sample pages 2 PDF (423.5 KB)
 Download Table of contents PDF (110.1 KB)
Recommended for you
Bibliographic Information
 Bibliographic Information

 Book Title
 Analysis and Enumeration
 Book Subtitle
 Algorithms for Biological Graphs
 Authors

 Andrea Marino
 Series Title
 Atlantis Studies in Computing
 Series Volume
 6
 Copyright
 2015
 Publisher
 Atlantis Press
 Copyright Holder
 Atlantis Press and the authors
 eBook ISBN
 9789462390973
 DOI
 10.2991/9789462390973
 Hardcover ISBN
 9789462390966
 Series ISSN
 22128557
 Edition Number
 1
 Number of Pages
 XVII, 151
 Number of Illustrations and Tables
 39 b/w illustrations
 Topics