Abstract
We study here dynamic antagonism in a fixed network, represented as a graph G of n vertices. In particular, we consider the case of k ≤n particles walking randomly independently around the network. Each particle belongs to exactly one of two antagonistic species, none of which can give birth to children. When two particles meet, they are engaged in a (sometimes mortal) local fight. The outcome of the fight depends on the species to which the particles belong. Our problem is to predict (i.e. to compute) the eventual chances of species survival. We prove here that this can indeed be done in expected polynomial time on the size of the network, provided that the network is undirected.
This work was partially supported by the IST Programme of the European Union under contact number IST-2005-15964 (AEOLUS) and by the Programme PENED under contact number 03ED568, co-funded 75% by European Union – European Social Fund (ESF), 25% by Greek Government – Ministry of Development – General Secretariat of Research and Technology (GSRT), and by Private Sector, under Measure 8.3 of O.P. Competitiveness – 3rd Community Support Framework (CSF).
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Nikoletseas, S., Raptopoulos, C., Spirakis, P. (2007). The Survival of the Weakest in Networks. In: Erlebach, T., Kaklamanis, C. (eds) Approximation and Online Algorithms. WAOA 2006. Lecture Notes in Computer Science, vol 4368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11970125_25
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DOI: https://doi.org/10.1007/11970125_25
Publisher Name: Springer, Berlin, Heidelberg
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