Abstract
Dominating sets in their many variations model a wealth of optimization problems like facility location or distributed file sharing. For instance, when a request can occur at any node in a graph and requires a server at that node, a minimum dominating set represents a minimum set of servers that serve an arbitrary single request by moving a server along at most one edge. This paper studies domination problems for two requests. For the problem of placing a minimum number of servers such that two requests at different nodes can be served with two different servers (called win-win), we present a logarithmic approximation, and we prove that nothing better is possible. We show that the same is true for Roman domination, the well studied problem variant that asks for each vertex to either possess its own server or to have a neighbor with two servers. Still the same is true if each idle server can move along one edge while the first of both requests is being served. For planar graphs, we propose a PTAS for Roman domination (and show that nothing better exists), and we get a constant approximation for win-win.
This work was partially supported by the Swiss Federal Office for Education and Science under the Human Potential Programme of the European Union under contract no. HPRNCT-1999-00104 (AMORE).
Part of this work was done while this author was with the University of Liverpool, supported by EPSRC grant GR/N09855, and also with the National Technical University of Athens.
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Pagourtzis, A., Penna, P., Schlude, K., Steinhöfel, K., Taylor, D.S., Widmayer, P. (2002). Server Placements, Roman Domination and Other Dominating Set Variants. In: Baeza-Yates, R., Montanari, U., Santoro, N. (eds) Foundations of Information Technology in the Era of Network and Mobile Computing. IFIP — The International Federation for Information Processing, vol 96. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35608-2_24
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DOI: https://doi.org/10.1007/978-0-387-35608-2_24
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