18686062
Sequencing-by-hybridization revisited: the analog-spectrum proposal
All published approaches to DNA sequencing by hybridization (SBH) consist of the biochemical acquisition of the spectrum of a target sequence (the set of its subsequences conforming to a given probing pattern) followed by the algorithmic reconstruction of the sequence from its spectrum. In the "standard" or "uniform" approach, the probing pattern is a string of length L and the length of reliably reconstructible sequences is known to be m/sub len/ = O(2/sup L/). For a fixed microarray area, higher sequencing performance can be achieved by inserting nonprobing gaps ("wild-cards") in the probing pattern. The reconstruction, however, must cope with the emergence of fooling probes due to the gaps and algorithmic failure occurs when the spectrum becomes too densely populated, although we can achieve m/sub comp/ = O(4/sup L/). Despite the combinatorial success of gapped probing, all current approaches are based on a biochemically unrealistic spectrum-acquisition model (digital-spectrum). The reality of hybridization is much more complex. Departing from the conventional model, in this paper, we propose an alternative, called the analog-spectrum model, which more closely reflects the biochemical process. This novel modeling reestablishes probe length as the performance-governing factor, adopting "semidegenerate bases" as suitable emulators of currently inadequate universal bases. One important conclusion is that accurate biochemical measurements are pivotal to the success of SBH. The theoretical proposal presented in this paper should be a convincing stimulus for the needed biotechnological work.
1952504
Data structures and algorithms for the string statistics problem
Given a textstringx of lengthn, theMinimal Augmented Suffix Tree T (x) ofx is a digital-search index that returns, for anyquery stringw and in a number of comparisons bounded by the length ofw, the maximum number of nonoverlapping occurrences ofw inx. It is shown that, denoting the length ofx byn, T(x) can be built in timeO(n log2n) and spaceO(n logn), off-line on a RAM.
206621028
Efficient Parallel Evaluation of Boolean Expressions
A Boolean expression wilth n literals, i.e., n distinct appearances of variables, can be evaluated by a parallel processing system in at most 1.81 log2n steps, or, equivalently, by a network constructed with two-input AND and OR gates and having at most 1.81 log2n levels.
155774
Evaluating the cylindricity of a nominally cylindrical point set
The minimum zone cylinder of a set of points in three dimensions is the cylindric crown defined by a pair of coaxial cylinders with minimal radial separation (width). In the context of tolerancing metrology, the set of points is nominally cylindrical, i.e., the points are known to lie in close proximity of a known reference cylinder. Using approximations which are valid only in the neighborhood of the reference cylinder, we can get a very good approximation of the minimum zone cylinder. The process provides successive approximations, and each iteration involves the solution of a linear programming problem in six dimensions. The error between the approximation and the optimal solution converges very rapidly (typically in three iterations in practice) down to a limit error of (8 omega^2)/R ( where omega is the width and R is the external radius of the zone cylinder).
28911111
Tetrahedrizing Point Sets in Three Dimensions
This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are coplanar. It also presents an algorithm that in O(nlog n) time constructs a tetrahedrization of a set of n points consisting of at most 3n–11 tetrahedra.
34573122
Corrigendum: A Fast Stable Sorting Algorithm with Absolutely Minimum Storage
Abstract An algorithm is described which sorts n numbers in place with the property of stability, i.e., preserving the original order of equal elements. The algorithm requires absolutely minimum storage 0 (log 2 n ) bits for program variables and a computation time at most 0 ( n (log 2 n ) 2 ).