@MISC{Bogdanov_miningevolving, author = {Petko Bogdanov and Ambuj K. Singh}, title = {Mining evolving network processes Supplemental material}, year = {} }

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Abstract

The single-snapshot MINESMOOTH problem is called Heaviest Subgraph (HS) and has been shown to be equiv-alent to the Prize Collecting Steiner Tree (PCST) prob-lem1 [5], which considers nodes with non-negative weights (prizes) and edges with negative weights (costs). An HS in-stance can be reduced to a PCST instance by (i) considering only non-negative edges and computing connected compo-nents in the resulting graph, and then (ii) collapsing each non-negative component into a single node that accumulates all corresponding positive edge weights [2]. Note that in PCST the node prize can be zero (a zero node) or positive (a positive node). The rooted PCST problem further imposes that a par-ticular node (root) belongs to the solution. Both PCST and rooted PCST are NP-hard and the latter cannot be approximated within any constant factor [4]. However, both ones can be solved in linear time on trees [6]. II. NP-HARDNESS OF α-MINESMOOTH