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Books > Science & Mathematics > Biology, life sciences > Life sciences: general issues
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Analysis and Enumeration - Algorithms for Biological Graphs (Hardcover, 2015 ed.)
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Analysis and Enumeration - Algorithms for Biological Graphs (Hardcover, 2015 ed.)
Series: Atlantis Studies in Computing, 6
Expected to ship within 12 - 17 working days
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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 brute-force 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 protein-protein 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 vertex-disjoint
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 RNA-seq
data.
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