3,987 research outputs found
Fast Algorithm for Partial Covers in Words
A factor of a word is a cover of if every position in lies
within some occurrence of in . A word covered by thus
generalizes the idea of a repetition, that is, a word composed of exact
concatenations of . In this article we introduce a new notion of
-partial cover, which can be viewed as a relaxed variant of cover, that
is, a factor covering at least positions in . We develop a data
structure of size (where ) that can be constructed in time which we apply to compute all shortest -partial covers for a
given . We also employ it for an -time algorithm computing
a shortest -partial cover for each
Partial match queries in relaxed K-dt trees
The study of partial match queries on random hierarchical multidimensional data structures dates back to Ph. Flajolet and C. Puechâs 1986 seminal paper on partial match retrieval. It was not until recently that fixed (as opposed to random) partial match queries were studied for random relaxed K-d trees, random standard K-d trees, and random 2-dimensional quad trees. Based on those results it seemed
natural to classify the general form of the cost of fixed partial match queries into two families: that of either random hierarchical structures or perfectly balanced structures, as conjectured by Duch, Lau and MartĂnez (On the Cost of Fixed Partial Queries in K-d trees Algorithmica, 75(4):684â723, 2016). Here we show that the conjecture just mentioned does not hold by introducing relaxed K-dt trees and providing the average-case analysis for random partial match queries as well as some advances on the average-case analysis for fixed partial match queries on them. In fact this cost âfor fixed partial match queriesâ does not follow the conjectured forms.Peer ReviewedPostprint (author's final draft
Data-Collection for the Sloan Digital Sky Survey: a Network-Flow Heuristic
The goal of the Sloan Digital Sky Survey is ``to map in detail one-quarter of
the entire sky, determining the positions and absolute brightnesses of more
than 100 million celestial objects''. The survey will be performed by taking
``snapshots'' through a large telescope. Each snapshot can capture up to 600
objects from a small circle of the sky. This paper describes the design and
implementation of the algorithm that is being used to determine the snapshots
so as to minimize their number. The problem is NP-hard in general; the
algorithm described is a heuristic, based on Lagriangian-relaxation and
min-cost network flow. It gets within 5-15% of a naive lower bound, whereas
using a ``uniform'' cover only gets within 25-35%.Comment: proceedings version appeared in ACM-SIAM Symposium on Discrete
Algorithms (1998
On largest volume simplices and sub-determinants
We show that the problem of finding the simplex of largest volume in the
convex hull of points in can be approximated with a factor
of in polynomial time. This improves upon the previously best
known approximation guarantee of by Khachiyan. On the other hand,
we show that there exists a constant such that this problem cannot be
approximated with a factor of , unless . % This improves over the
inapproximability that was previously known. Our hardness result holds
even if , in which case there exists a \bar c\,^{d}-approximation
algorithm that relies on recent sampling techniques, where is again a
constant. We show that similar results hold for the problem of finding the
largest absolute value of a subdeterminant of a matrix
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