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Fast Partial Subset Convolution for Steiner Tree Problem

We present a new algorithm that solves the minimum Steiner tree problem on an undirected graph with n nodes, k terminals, and m edges with bounded integer weights in time Õ((2− ε)n + nm). Our algorithm beats the aesthetically appealing and seemingly inherent 2 bound of the current best algorithm for Steiner tree problem from Björklund, Husfeldt, Kaski, and Koivisto. Our algorithm is based on fast subset convolution and a variant of the classical tree-separator theorem.