Axiomatic analysis of liability problems with rooted-tree networks in tort law

2022 ◽  
Author(s):  
Takayuki Oishi ◽  
Gerard van der Laan ◽  
René van den Brink
Keyword(s):  
Rooted Tree ◽  
Tort Law ◽  
Tree Networks ◽  
Axiomatic Analysis

scholarly journals Constant time per edge is optimal on rooted tree networks

1997 ◽  
Vol 10 (4) ◽  
pp. 189-197 ◽  
Author(s):  
Michael Mitzenmacher
Keyword(s):  
Rooted Tree ◽  
Constant Time ◽  
Tree Networks

OPTIMALITY AND SELF-STABILIZATION IN ROOTED TREE NETWORKS

1999 ◽  
Vol 09 (03) ◽  
pp. 313-323
Author(s):  
FRANCK PETIT ◽  
VINCENT VILLAIN
Keyword(s):  
Rooted Tree ◽  
The State ◽  
Extra Cost ◽  
Tree Networks ◽  
Token Circulation ◽  
Self Stabilization ◽  
Legitimate State ◽  
Arbitrary Tree

In this paper, we consider arbitrary tree networks where every processor, except one, called the root, executes the same program. We show that, to design a depth-first token circulation protocol in such networks, it is necessary to have at least [Formula: see text] configurations, where n is the number of processors in the network and Δi is the degree of processor pi. We then propose a depth-first token circulation algorithm which matches the above minimal number of configurations. We show that the proposed algorithm is self-stabilizing, i.e., the system eventually recovers itself to a legitimate state after any perturbation modifying the state of the processors. Hence, the proposed algorithm is optimal in terms of the number of configurations and no extra cost is involved in making it stabilizing.

scholarly journals An Axiomatic Analysis of Joint Liability Problems with Rooted Tree Structure

2016 ◽  
Author(s):  
Takayuki Oishi ◽  
Gerard van der Laan ◽  
Rene van den Brink
Keyword(s):  
Rooted Tree ◽  
Tree Structure ◽  
Joint Liability ◽  
Axiomatic Analysis

OPTIMALITY AND SELF-STABILIZATION IN ROOTED TREE NETWORKS

2000 ◽  
Vol 10 (01) ◽  
pp. 3-14 ◽  
Author(s):  
FRANCK PETIT ◽  
VINCENT VILLAIN
Keyword(s):  
Rooted Tree ◽  
The State ◽  
Extra Cost ◽  
Tree Networks ◽  
Token Circulation ◽  
Self Stabilization ◽  
Legitimate State ◽  
Arbitrary Tree

In this paper, we consider arbitrary tree networks where every processor, except one, called the root, executes the same program. We show that, to design a depth-first token circulation protocol in such networks, it is necessary to have at least [Formula: see text] configurations, where n is the number of processors in the network and Δi is the degree of processor pi. We then propose a depth-first token circulation algorithm which matches the above minimal number of configurations. We show that the proposed algorithm is self-stabilizing, i.e., the system eventually recovers itself to a legitimate state after any perturbation modifying the state of the processors. Hence, the proposed algorithm is optimal in terms of the number of configurations and no extra cost is involved in making it stabilizing.

Sign in / Sign up

Export Citation Format

Share Document