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We have developed a phylogenetic tree reconstruction method that detects and reports multiple topologically distant low-cost solutions. Our method is a generalization of the neighbor-joining method of Saitou and Nei and affords a more thorough sampling of the solution space by keeping track of multiple partial solutions during its execution. The scope of… (More)

We solve a discrete version of the classic Plateau problem, which asks for a minimal surface spanning a given curve. Our algorithm is based on a network-flow formulation that finds minimal slabs, intuitively corresponding to minimal "surfaces" of prescribed thickness. We let the slab thickness approach zero in order to obtain the desired minimal surface.

We discuss a new minimum density objective for spanning and Steiner tree constructions. This formulation is motivated by the minimum-area layout objective, which is best achieved through balancing the usage of horizontal and vertical routing resources. We present two efficient heuristics for constructing low-density spanning trees and prove that their… (More)

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