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- W2912105786 abstract "In this paper, we define a new problem called the Maximum Connectivity Improvement (MCI) problem: given a directed graph (G = (V,E)), a weight function (w:V rightarrow mathbb {N}_{ge 0}), a profit function (p:V rightarrow mathbb {N}_{ge 0}), and an integer B, find a set S of at most B edges not in E that maximises (f(S)=sum _{vin V}w_vcdot p(R(v,S))), where p(R(v, S)) is the sum of the profits of the nodes reachable from node v when the edges in S are added to G. We first show that we can focus on Directed Acyclic Graphs (DAG) without loss of generality. We prove that the MCI problem on DAG is ( NP )-Hard to approximate to within a factor greater than (1-1/e) even if we restrict to graphs with a single source or a single sink, and MCI remains ( NP )-Complete if we further restrict to unitary weights. We devise a polynomial time algorithm based on dynamic programming to solve the MCI problem on trees with a single source. We propose a polynomial time greedy algorithm that guarantees ((1-1/e))-approximation ratio on DAGs with a single source or a single sink." @default.
- W2912105786 created "2019-02-21" @default.
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- W2912105786 date "2019-01-01" @default.
- W2912105786 modified "2023-10-11" @default.
- W2912105786 title "On the Maximum Connectivity Improvement Problem" @default.
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- W2912105786 doi "https://doi.org/10.1007/978-3-030-14094-6_4" @default.
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