Minimum Sum Set Cover: Structures and Algorithm
Zhongyi Zhang, Yixin Cao

Abstract
A set cover of a hypergraph is a set of vertices intersecting every hyperedge. In the minimum sum set cover problem, vertices are selected one by one; each edge pays the position of the first vertex that hits it, and the objective is to minimize the total cost. When is a graph, this is the minimum sum vertex cover problem. A solution is specified by a set cover together with an ordering of its vertices. While the classical set cover problem seeks to minimize , the minimum sum variant favors covering many edges early and may prefer larger covers. This motivates a natural question: how large can the gap between~ and be? We prove an upper bound , and show that for any positive~, there exists a hypergraph on vertices with and . For…
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