25,679 research outputs found
Priority Queues with Multiple Time Fingers
A priority queue is presented that supports the operations insert and
find-min in worst-case constant time, and delete and delete-min on element x in
worst-case O(lg(min{w_x, q_x}+2)) time, where w_x (respectively q_x) is the
number of elements inserted after x (respectively before x) and are still
present at the time of the deletion of x. Our priority queue then has both the
working-set and the queueish properties, and more strongly it satisfies these
properties in the worst-case sense. We also define a new distribution-sensitive
property---the time-finger property, which encapsulates and generalizes both
the working-set and queueish properties, and present a priority queue that
satisfies this property.
In addition, we prove a strong implication that the working-set property is
equivalent to the unified bound (which is the minimum per operation among the
static finger, static optimality, and the working-set bounds). This latter
result is of tremendous interest by itself as it had gone unnoticed since the
introduction of such bounds by Sleater and Tarjan [JACM 1985]. Accordingly, our
priority queue satisfies other distribution-sensitive properties as the static
finger, static optimality, and the unified bound.Comment: 14 pages, 4 figure
Implementation and complexity of the watershed-from-markers algorithm computed as a minimal cost forest
The watershed algorithm belongs to classical algorithms in mathematical
morphology. Lotufo et al. published a principle of the watershed computation by
means of an Image Foresting Transform (IFT), which computes a shortest path
forest from given markers. The algorithm itself was described for a 2D case
(image) without a detailed discussion of its computation and memory demands for
real datasets. As IFT cleverly solves the problem of plateaus and as it gives
precise results when thin objects have to be segmented, it is obvious to use
this algorithm for 3D datasets taking in mind the minimizing of a higher memory
consumption for the 3D case without loosing low asymptotical time complexity of
O(m+C) (and also the real computation speed). The main goal of this paper is an
implementation of the IFT algorithm with a priority queue with buckets and
careful tuning of this implementation to reach as minimal memory consumption as
possible.
The paper presents five possible modifications and methods of implementation
of the IFT algorithm. All presented implementations keep the time complexity of
the standard priority queue with buckets but the best one minimizes the costly
memory allocation and needs only 19-45% of memory for typical 3D medical
imaging datasets. Memory saving was reached by an IFT algorithm simplification,
which stores more elements in temporary structures but these elements are
simpler and thus need less memory.
The best presented modification allows segmentation of large 3D medical
datasets (up to 512x512x680 voxels) with 12-or 16-bits per voxel on currently
available PC based workstations.Comment: v1: 10 pages, 6 figures, 7 tables EUROGRAPHICS conference,
Manchester, UK, 2001. v2: 12 pages, reformated for letter, corrected IFT to
"Image Foresting Tranform
Strengthened Lazy Heaps: Surpassing the Lower Bounds for Binary Heaps
Let denote the number of elements currently in a data structure. An
in-place heap is stored in the first locations of an array, uses
extra space, and supports the operations: minimum, insert, and extract-min. We
introduce an in-place heap, for which minimum and insert take worst-case
time, and extract-min takes worst-case time and involves at most
element comparisons. The achieved bounds are optimal to within
additive constant terms for the number of element comparisons. In particular,
these bounds for both insert and extract-min -and the time bound for insert-
surpass the corresponding lower bounds known for binary heaps, though our data
structure is similar. In a binary heap, when viewed as a nearly complete binary
tree, every node other than the root obeys the heap property, i.e. the element
at a node is not smaller than that at its parent. To surpass the lower bound
for extract-min, we reinforce a stronger property at the bottom levels of the
heap that the element at any right child is not smaller than that at its left
sibling. To surpass the lower bound for insert, we buffer insertions and allow
nodes to violate heap order in relation to their parents
Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls
We consider space-bounded computations on a random-access machine (RAM) where
the input is given on a read-only random-access medium, the output is to be
produced to a write-only sequential-access medium, and the available workspace
allows random reads and writes but is of limited capacity. The length of the
input is elements, the length of the output is limited by the computation,
and the capacity of the workspace is bits for some predetermined
parameter . We present a state-of-the-art priority queue---called an
adjustable navigation pile---for this restricted RAM model. Under some
reasonable assumptions, our priority queue supports and
in worst-case time and in worst-case time for any . We show how to use this
data structure to sort elements and to compute the convex hull of
points in the two-dimensional Euclidean space in
worst-case time for any . Following a known lower bound for the
space-time product of any branching program for finding unique elements, both
our sorting and convex-hull algorithms are optimal. The adjustable navigation
pile has turned out to be useful when designing other space-efficient
algorithms, and we expect that it will find its way to yet other applications.Comment: 21 page
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