Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees

Mehler A (2010)
In: Structural Analysis of Complex Networks. Dehmer M (Ed);Boston: Birkhäuser: 381-402.

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Book Chapter | Published | English
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Dehmer, Matthias
Abstract
This chapter introduces a novel class of graphs: Minimum Spanning Markovian Trees (MSMT). The idea behind MSMTs is to provide spanning trees that minimize the costs of edge traversals in a Markovian manner, that is, in terms of the path starting with the root of the tree and ending at the vertex under consideration. In a second part, the chapter generalizes this class of spanning trees in order to allow for damped Markovian effects in the course of spanning. These two effects - that is, (i) the sensitivity to the contexts generated by consecutive edges and (ii) the decreasing impact of more antecedent (or "weakly remembered") vertices - are well-known in cognitive modeling (Gaerdenfors, 2000; Kintsch, 1998; Murphy, 2002; Sharkey and Sharkey, 1992}. In this sense, the chapter can also be read as an effort to introduce a graph-model to support the simulation of cognitive systems. Note that MSMTs are not to be confused with branching Markov chains or Markov trees (Menshikov and Volkov 1997} as we focus on generating spanning trees from given weighted undirected networks.
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Mehler A. Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees. In: Dehmer M, ed. Structural Analysis of Complex Networks. Boston: Birkhäuser; 2010: 381-402.
Mehler, A. (2010). Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees. In M. Dehmer (Ed.), Structural Analysis of Complex Networks (pp. 381-402). Boston: Birkhäuser.
Mehler, A. (2010). “Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees” in Structural Analysis of Complex Networks, ed. M. Dehmer (Boston: Birkhäuser), 381-402.
Mehler, A., 2010. Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees. In M. Dehmer, ed. Structural Analysis of Complex Networks. Boston: Birkhäuser, pp. 381-402.
A. Mehler, “Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees”, Structural Analysis of Complex Networks, M. Dehmer, ed., Boston: Birkhäuser, 2010, pp.381-402.
Mehler, A.: Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees. In: Dehmer, M. (ed.) Structural Analysis of Complex Networks. p. 381-402. Birkhäuser, Boston (2010).
Mehler, Alexander. “Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees”. Structural Analysis of Complex Networks. Ed. Matthias Dehmer. Boston: Birkhäuser, 2010. 381-402.
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