The Total Acquisition Number Of The Randomly Weighted Path

• Autorzy: Anant Godbole , Elizabeth Kelley , Emily Kurtz , Paweł Prałat , Yiguang Zhang
• Języki publikacji: EN

Abstrakty

EN

There exists a significant body of work on determining the acquisition number at(G) of various graphs when the vertices of those graphs are each initially assigned a unit weight. We determine properties of the acquisition number of the path, star, complete, complete bipartite, cycle, and wheel graphs for variations on this initial weighting scheme, with the majority of our work focusing on the expected acquisition number of randomly weighted graphs. In particular, we bound the expected acquisition number E(at(Pn)) of the n-path when n distinguishable “units” of integral weight, or chips, are randomly distributed across its vertices between 0.242n and 0.375n. With computer support, we improve it by showing that E(at(Pn)) lies between 0.29523n and 0.29576n. We then use subadditivity to show that the limiting ratio lim E(at(Pn))/n exists, and simulations reveal more exactly what the limiting value equals. The Hoeffding-Azuma inequality is used to prove that the acquisition number is tightly concentrated around its expected value. Additionally, in a different context, we offer a non-optimal acquisition protocol algorithm for the randomly weighted path and exactly compute the expected size of the resultant residual set.

Słowa kluczowe

EN

total acquisition number; Poissonization; dePoissonization; Maxwell-Boltzman and Bose-Einstein allocation.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 4
• Strony: 919-934

Daty

wydano

2017-11-27

otrzymano

2015-08-14

poprawiono

2016-07-15

zaakceptowano

2016-07-15

online

2017-09-02

Twórcy

autor

Anant Godbole

• ,

autor

Elizabeth Kelley

• ,

autor

Emily Kurtz

• ,

autor

Paweł Prałat

• ,

autor

Yiguang Zhang

• ,

Identyfikatory

DOI

10.7151/dmgt.1972