Lossy Gossip and Composition of Metrics

被引：5
|
作者：
Brouwer, Andries E. [1 ]
Draisma, Jan [1 ]
Frenk, Bart J. [1 ]
机构：
[1] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2015年 / 53卷 / 04期
关键词：
Min-plus matrix multiplication; Finite metrics; Gossip; Tropical algebraic groups; OPTIMAL REALIZATIONS;
D O I：
10.1007/s00454-015-9666-1
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We study the monoid generated by distance matrices under tropical (or min-plus) multiplication. Using the tropical geometry of the orthogonal group, we prove that this monoid is a finite polyhedral fan of dimension , and we compute the structure of this fan for up to . The monoid captures gossip among gossipers over lossy phone lines, and contains the gossip monoid over ordinary phone lines as a submonoid. We prove several new results about this submonoid as well. In particular, we establish a sharp bound on chains of calls in each of which someone learns something new.
引用
收藏
页码：890 / 913
页数：24
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