# Approximation Algorithm for Survivable Network Design by qym17251

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```									     Approximation Algorithm for Survivable Network Design Problem

ID:350301069 Name:Hiroki Katsuya

abstract
The Survivable Network Design Problem           mial time, it has high time complexity in
(SNDP) is the problem, given an undirected        theory.
graph and a connectivity requirement func-          In this paper, we consider the graph the-
tion ruv for each pair u, v of vertices, to ﬁnd   oretic approximation algorithm for {2, 3}-
a minimum subgraph in which each pair u,          EC-SNDP. This algorithm is a combination
v of vertices is at least ruv connective. If      of the approximation algorithm for {1, 2}-
ruv is edge connectivity requirement func-        EC-SNDP using depth ﬁrst search (DFS)
tion, this problem is called the Edge Con-        (Krysta 2001) and the approximation al-
nectivity Survivable Network Design Prob-         gorithm for {k}-EC-SNDP using DFS and
lem (EC-SNDP), and if vertex connectiv-           maximal spanning forest (Khuller 1997).
ity requirement function, this problem is           Our algorithm works for the input in-
called the Vertex Connectivity Survivable         stance I = (G, {ruv }) as follows: it ﬁrst
Network Design Problem (VC-SNDP). If,             approximately solve the {1, 2}-EC-SNDP
for some set X, ruv ∈ X for each pair u,                          ′
for I ′ = (G, {ruv } : ruv = ruv − 1), and
′

v of vertices, we denote the problem as X-        add a maximal spanning forest to this so-
EC-SNDP. These problems are known to              lution. This algorithm is turned out to be
be NP-hard and thus approximation algo-           7/3-approximation.
rithms are of importance. The problem of            We further improve this algorithm by delet-
developing the breakdown tolerant network         ing the edges from the approximation solu-
is enumerated as an application example.          tion of the {1, 2}-EC-SNDP to I ′ and by
We concentrate on {2, 3}-EC-SNDP. For           improving the estimate of the optimal so-
EC-SNDP, Jain has given a 2-approximation         lution. The improved algorithm is turned
algorithm using linear programming relax-         out to be 2-approximation.
ation repeatedly. It is applicable in {2, 3}-
EC-SNDP. Although it can run in polyno-

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