312 research outputs found
Top-Down Skiplists
We describe todolists (top-down skiplists), a variant of skiplists (Pugh
1990) that can execute searches using at most
binary comparisons per search and that have amortized update time
. A variant of todolists, called working-todolists,
can execute a search for any element using binary comparisons and have amortized search time
. Here, is the "working-set number" of
. No previous data structure is known to achieve a bound better than
comparisons. We show through experiments that, if implemented
carefully, todolists are comparable to other common dictionary implementations
in terms of insertion times and outperform them in terms of search times.Comment: 18 pages, 5 figure
The Fresh-Finger Property
The unified property roughly states that searching for an element is fast
when the current access is close to a recent access. Here, "close" refers to
rank distance measured among all elements stored by the dictionary. We show
that distance need not be measured this way: in fact, it is only necessary to
consider a small working-set of elements to measure this rank distance. This
results in a data structure with access time that is an improvement upon those
offered by the unified property for many query sequences
An optimal randomized algorithm for d-variate zonoid depth
AbstractA randomized linear expected-time algorithm for computing the zonoid depth [R. Dyckerhoff, G. Koshevoy, K. Mosler, Zonoid data depth: Theory and computation, in: A. Prat (Ed.), COMPSTAT 1996—Proceedings in Computational Statistics, Physica-Verlag, Heidelberg, 1996, pp. 235–240; K. Mosler, Multivariate Dispersion, Central Regions and Depth. The Lift Zonoid Approach, Lecture Notes in Statistics, vol. 165, Springer-Verlag, New York, 2002] of a point with respect to a fixed dimensional point set is presented
The Price of Order
We present tight bounds on the spanning ratio of a large family of ordered
-graphs. A -graph partitions the plane around each vertex into
disjoint cones, each having aperture . An ordered
-graph is constructed by inserting the vertices one by one and
connecting each vertex to the closest previously-inserted vertex in each cone.
We show that for any integer , ordered -graphs with
cones have a tight spanning ratio of . We also show that for any integer , ordered
-graphs with cones have a tight spanning ratio of . We provide lower bounds for ordered -graphs with and cones. For ordered -graphs with and
cones these lower bounds are strictly greater than the worst case spanning
ratios of their unordered counterparts. These are the first results showing
that ordered -graphs have worse spanning ratios than unordered
-graphs. Finally, we show that, unlike their unordered counterparts,
the ordered -graphs with 4, 5, and 6 cones are not spanners
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