A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On calculating connected dominating set for efficient routing in ad hoc wireless networks
DIALM '99 Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications
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Consider a connected graph G=(V,E). For a pair of nodes u and v, denote by M uv the set of intermediate nodes of a shortest path between u and v. We are intertested in minimization of the union 驴 u,v驴V M uv . We will show that this problem is NP-hard and cannot have polynomial-time 驴ln驴-approximation for 0驴n O(loglogn)) where 驴 is the maximum node degree of input graph. We will also construct a polynomial-time $H(\frac{\delta (\delta -1)}{2})$ -approximation for the problem where H(驴) is the harmonic function.