Improved Approximation Algorithm for the Fault-Tolerant Facility Placement Problem with Rejection

2019 ◽  
Vol 39 (2) ◽  
pp. 122-128
Author(s):  
Shuaijing Yu
Keyword(s):  
Approximation Algorithm ◽  
Fault Tolerant ◽  
Placement Problem ◽  
Facility Placement

On the Bounded Fault-Tolerant Facility Placement Problem

2018 ◽  
Vol 38 (3) ◽  
pp. 241-249
Author(s):  
Qiaoqiao Zhu ◽  
Yizhe Zhu ◽  
Jun Yang ◽  
Wenchang Luo
Keyword(s):  
Fault Tolerant ◽  
Placement Problem ◽  
Facility Placement

scholarly journals Constant Factor Approximation for Tracking Paths and Fault Tolerant Feedback Vertex Set

2021 ◽  
pp. 23-38
Author(s):  
Václav Blažej ◽  
Pratibha Choudhary ◽  
Dušan Knop ◽  
Jan Matyáš Křišt’an ◽  
Ondřej Suchý ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Fault Tolerant ◽  
Minimum Weight ◽  
Weighted Graph ◽  
Constant Factor ◽  
Weighted Graphs ◽  
Feedback Vertex Set ◽  
Fixed Integer ◽  
Vertex Set

AbstractConsider a vertex-weighted graph G with a source s and a target t. Tracking Paths requires finding a minimum weight set of vertices (trackers) such that the sequence of trackers in each path from s to t is unique. In this work, we derive a factor 66-approximation algorithm for Tracking Paths in weighted graphs and a factor 4-approximation algorithm if the input is unweighted. This is the first constant factor approximation for this problem. While doing so, we also study approximation of the closely related r-Fault Tolerant Feedback Vertex Set problem. There, for a fixed integer r and a given vertex-weighted graph G, the task is to find a minimum weight set of vertices intersecting every cycle of G in at least $$r+1$$ r + 1 vertices. We give a factor $$\mathcal {O}(r^2)$$ O ( r 2 ) approximation algorithm for r-Fault Tolerant Feedback Vertex Set if r is a constant.

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