Large surveys using multiobject spectrographs require automated methods for deciding how to efficiently point observations and how to assign targets to each pointing. The Sloan Digital Sky Survey (SDSS) will observe around 10 6 spectra from targets distributed over an area of about 10,000 deg 2 , using a multiobject fiber spectrograph that can simultaneously observe 640 objects in a circular field of view (referred to as a '' tile '') 1=49 in radius. No two fibers can be placed closer than 55 00 during the same observation; multiple targets closer than this distance are said to '' collide.'' We present here a method of allocating fibers to desired targets given a set of tile centers that includes the effects of collisions and that is nearly optimally efficient and uniform. Because of large-scale structure in the galaxy distribution (which form the bulk of the SDSS targets), a naive covering of the sky with equally spaced tiles does not yield uniform sampling. Thus, we present a heuristic for perturbing the centers of the tiles from the equally spaced distribution that provides more uniform completeness. For the SDSS sample, we can attain a sampling rate of greater than 92% for all targets, and greater than 99% for the set of targets that do not collide with each other, with an efficiency greater than 90% (defined as the fraction of available fibers assigned to targets). The methods used here may prove useful to those planning other large surveys.
This paper studies the problem of routing wires in a grid among features on one layer of a VLSI chip, when a sketch of the layer is given. A sketch specifies the positions of features and the topology of the interconnecting wires. We give polynomial-time algorithms that (1) determine the routability of a sketch, and (2) produce a routing of a sketch that. optimizes both individual and total wire length. These algorithms subsume most of the polynomial-time algorithms in the literature for planar routing and routability testing in the rectilinear grid model. We also provide au explicit construction of a database, called the rubber-band eguiualent, to support computation involving the layout topology.
We provide a linear-time algorithm for determining the minimum separation required to route a channel when the connections can be realized in one layer. Differing from the usual "river-routing" context, we allow single-sided connections. The algorithm also works directly for problems with multiterminal nets and does not require wires to lie on an underlying grid, though it does use the rectilinear wiring model. The approach can also be used to obtain a routability test for single-layer switchboxes that corrects errors in the literature and is simpler than other correct approaches. These problems are of interest because they may arise as subtasks in routing problems involving more than one layer.
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