Showing papers by "Richard Durbin published in 1986"
TL;DR: In this paper, the problem of finding the numberings which minimize the edgesum of a given number of vertices in a graph has been shown to be NP-hard in the special case where the graph is the $2^n $ cube and for several instances of graphs with high degrees of symmetry.
Abstract: Given a numbering of the vertices of a graph, one can define the edgesum [6] as the sum of differences between adjacent vertices. The problem of finding numberings which are optimal in the sense of minimizing the edgesum is NP-complete [2] but has been solved in the special case where the graph is the $2^n $ cube [3] and for several instances of graphs with high degrees of symmetry [6]. We find the solutions for numberings of an $N \times N$ array. These have practical application in the problem of representing spatial information in a one-dimensional medium. To find our solutions, we exploit the fact that such numberings can always be taken to be ordered, in the sense that numbers increase along rows and down columns. We also consider a generalization of this problem to the case where the differences are raised to a power q. We derive bounds on the edgesum in this case, and show that the optimal numberings for $q < 1$ must be essentially different from those we have found for $q = 1$. While the latter ma...
116 citations
TL;DR: Isomorphous and anomalous difference Pattersons, based on detector data, are shown for a variable surface glycoprotein mercury derivative and for a repressor-DNA bromine derivative, which has been solved at 7 angstroms with detector data only.
Abstract: A set of programs has been developed for rapid collection of x-ray intensity data from protein and virus crystals with a commercially available two-dimensional focused geometry electronic detector. The detector is compact and portable, with unusually high spatial resolution comparable to that used in oscillation photography. It has allowed x-ray data collection on weakly diffracting crystals with large unit cells, as well as more conventional "diffractometer-quality" crystals. The quality of the data is compared with that from oscillation photography and automated diffractometry in the range of unit cells from 96.3 to 383.2 angstroms. Isomorphous and anomalous difference Pattersons, based on detector data, are shown for a variable surface glycoprotein mercury derivative and for a repressor-DNA bromine derivative, which has been solved at 7 angstroms with detector data only.
71 citations