The P-Value for Cost Sharing in Minimum Cost Spanning Tree Situations

Additivity in minimum cost spanning tree problems

“…Our paper is very related to the paper of Brânzei et al (2004) because they also characterize this rule using an additivity property and other two properties: equal treatment and upper bound contributions. These properties are very related to the concept of C-component.…”

“…In mcstp there exists an additivity property called cone-wise positive linearity (CP L) , which has been introduced by Brânzei et al (2004). We say that ψ satis-…”

Obligation rules for minimum cost spanning tree situations and their monotonicity properties

“…The P -value (Branzei et al (2003)) and the P τ -values, with τ ∈ Σ N , introduced in Norde et al (2004) and studied in Branzei et al(2003), are Obligation rules. In fact φô * (w) = P (w) and φô τ (w) = P , with σ ∈ Σ E N such that w ∈ K σ .…”

“…It turns out that particular rules in this class are the P -value (Branzei et al (2003)) and the P τ -values, for each ordering τ of the players ). Moreover it is shown that the P -value is the average of the P τ -values over all the possible orderings τ .…”

Minimum cost arborescences

“…6 This is a term coined by because this allocation rule has been independently proposed and analyzed in a number of papers. See, for instance, Bergantinos and Vidal-Puga (2007a), Bergantinos and Vidal-Puga (2007b), , Branzei et al (2004), Feltkamp et al (1994, Norde et al (2001) Branzei et al (2005).…”