The Checkpoint Problem

In this paper, we consider the checkpoint problem in which given an undirected graph G, a set of sourcedestinations {(s1, t1), (s1, t1), . . . , (sk, tk)} and a set of fixed paths P between them, the goal is to find a set of checkpoint edges E which disconnect each si from ti and minimize the sum (equivalently average) or maximum intersection with each path p P. This problem has several natural applications, e.g., in urban transportation and network security, and in a sense combines the multicut problem and the minimum membership set cover problem. We show that for the sum version, any approximation for the undirected multicut problem gives a approximation for the checkpoint problem and visa-versa, and thus there exists an O(log n) approximation and a non-constant hardness under Unique Game Conjecture for this problem. Our current approximability results for the max version have a wide gap: we can show an approximation factor of O( n log n opt ) and a hardness of 2 under P = NP for...

• Type: Conference
• Year: 2010
• Where: APPROX
• Authors: MohammadTaghi Hajiaghayi, Rohit Khandekar, Guy Kortsarz, Julián Mestre
• Keywords: Algorithms, APPROX 2010, Checkpoint Problem, Hardness, Multicut Problem