Finding the Optimal Shortest Path Tree with Respect to Single Link Failure Recovery

This paper investigates the shortest paths tree problem taking single link failure into account. Let G be a graph modeled by network with vertex set V and edge set E. Given a specified vertex s. A shortest paths tree T
_s
={e
₁
, e
₂
,
_hellip
, e
_n-1
} rooted at s satisfies the path from s to u
_i
in T
_s
is a shortest path in G, where e
_i
=(u
_i
, v
_i
) and u
_i
=parent(v
_i
). Let |P
_G
(s,t)| be the cost of the shortest (s, t)-path in graph G. A shortest (s,t)-path P is optimal with respect to single link failure if max
_{foralle=(x,y)isinE(P)}
|P
_G\e
(x,t)| is minimum among all the shortest (s,t)-paths. A shortest paths tree is optimal if it consists of optimal shortest paths. We present an algorithm that takes O(|V| |E|+|V|
²
log|V|) time to build the shortest paths tree. Our result is applicable to the route design in the communication network when single link failure is considered.