---
res:
bibo_abstract:
- 'Evolution occurs in populations of reproducing individuals. The structure of
the population affects the outcome of the evolutionary process. Evolutionary graph
theory is a powerful approach to study this phenomenon. There are two graphs.
The interaction graph specifies who interacts with whom in the context of evolution.
The replacement graph specifies who competes with whom for reproduction. The vertices
of the two graphs are the same, and each vertex corresponds to an individual.
A key quantity is the fixation probability of a new mutant. It is defined as the
probability that a newly introduced mutant (on a single vertex) generates a lineage
of offspring which eventually takes over the entire population of resident individuals.
The basic computational questions are as follows: (i) the qualitative question
asks whether the fixation probability is positive; and (ii) the quantitative approximation
question asks for an approximation of the fixation probability. Our main results
are: (1) We show that the qualitative question is NP-complete and the quantitative
approximation question is #P-hard in the special case when the interaction and
the replacement graphs coincide and even with the restriction that the resident
individuals do not reproduce (which corresponds to an invading population taking
over an empty structure). (2) We show that in general the qualitative question
is PSPACE-complete and the quantitative approximation question is PSPACE-hard
and can be solved in exponential time.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Krishnendu
foaf_name: Chatterjee, Krishnendu
foaf_surname: Chatterjee
foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-4561-241X
- foaf_Person:
foaf_givenName: Rasmus
foaf_name: Ibsen-Jensen, Rasmus
foaf_surname: Ibsen-Jensen
foaf_workInfoHomepage: http://www.librecat.org/personId=3B699956-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0003-4783-0389
- foaf_Person:
foaf_givenName: Martin
foaf_name: Nowak, Martin
foaf_surname: Nowak
bibo_doi: 10.15479/AT:IST-2014-190-v2-2
dct_date: 2014^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/2664-1690
dct_language: eng
dct_publisher: IST Austria@
dct_title: The complexity of evolution on graphs@
...