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- graph and network algorithms
- computational complexity
- domination theory
- facility location in networks
- graph connectivity and reliability
- network modeling of facilities for safeguards (e.g., fire safety) studies
Sample Project: Optimal Facility Location in Networks
Decision problems involving the optimal selection of one or more sites at which to locate facilities are of interest to researchers in many areas including mathematics, operations research, logistics, economics and computer science. The following illustrates a competitive location theory problem.
Assume the above graph G has one customer at each of the 15 vertices and each of the 17 indicated edges vivj has length one. Player A is to select a vertex at which to build a store, and subsequently Player Bmust choose a different vertex for a similar store. Each customer will shop at the nearer store, and a customer equidistant from both stores will shop at each one-half of the time. Each player wants to maximize his/her number of customers. For example, if A chooses v7 and B then chooses v1, then A gets
customers and B gets 15 − 7 = 8 customers. Player B wins! Where should A actually choose to locate a store?
Full Refereed Publication List
- Fundamentals of Domination in Graphs, Marcel Dekker, Inc., 1998, T.W.Haynes, S.T.Hedetniemi and P.J.Slater.
- Domination in Graphs Advanced Topics, Marcel Dekker, Inc., 1998, eds. T.W.Haynes. S.T.Hedetniemi and P.J.Slater
- F. Allen O'Neal, Neighborhood Sum Parameters on Graphs, UAH, 2011
- Miranda Roden, Liar's Domination and the Domination Continuum, UAH 2009
- Ann Sinko, Generalized Graph Parameters, UAH 2008
- Yan Wang, Acquisition Numbers and Competition-Acquisition Numbers, UAH 2005
- James B Phillips, Colored Distance and Competition Parameters, UAH 2002
- Eric L. Trees, The LP Matrix Partition Theorem and its Use with Fractional Domination and Domatic Parameters, UAH 2000
- Douglas E. Lampert, Independence Related Graph Parameters, UAH, 1998.
- Christian B. Smart, Studies of Graph Based LP/IP Parameters, UAH, 1996.
- Dana Grinstead, Algorithmic Templates and Multiset Problems in Graphs, UAH, 1989.
- M.S. and Ph.D. (math) The University of Iowa
- M.S. (computer science) UAH
- B.S. (math) Iona College
Following a year as an NRC Postdoctoral Fellow at the National Bureau of Standards and six years in the Applied Math Division at Sandia Laboratories, Dr. Slater joined UAH in 1981. He is the author/co-author of over 200 refereed publications.
- ballroom dancing
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