17,660 research outputs found
Selection from read-only memory with limited workspace
Given an unordered array of elements drawn from a totally ordered set and
an integer in the range from to , in the classic selection problem
the task is to find the -th smallest element in the array. We study the
complexity of this problem in the space-restricted random-access model: The
input array is stored on read-only memory, and the algorithm has access to a
limited amount of workspace. We prove that the linear-time prune-and-search
algorithm---presented in most textbooks on algorithms---can be modified to use
bits instead of words of extra space. Prior to our
work, the best known algorithm by Frederickson could perform the task with
bits of extra space in time. Our result separates
the space-restricted random-access model and the multi-pass streaming model,
since we can surpass the lower bound known for the latter
model. We also generalize our algorithm for the case when the size of the
workspace is bits, where . The running time
of our generalized algorithm is ,
slightly improving over the
bound of Frederickson's algorithm. To obtain the improvements mentioned above,
we developed a new data structure, called the wavelet stack, that we use for
repeated pruning. We expect the wavelet stack to be a useful tool in other
applications as well.Comment: 16 pages, 1 figure, Preliminary version appeared in COCOON-201
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
Time-Space Trade-Offs for Computing Euclidean Minimum Spanning Trees
In the limited-workspace model, we assume that the input of size lies in
a random access read-only memory. The output has to be reported sequentially,
and it cannot be accessed or modified. In addition, there is a read-write
workspace of words, where is a given parameter.
In a time-space trade-off, we are interested in how the running time of an
algorithm improves as varies from to .
We present a time-space trade-off for computing the Euclidean minimum
spanning tree (EMST) of a set of sites in the plane. We present an
algorithm that computes EMST using time and
words of workspace. Our algorithm uses the fact that EMST is a subgraph of
the bounded-degree relative neighborhood graph of , and applies Kruskal's
MST algorithm on it. To achieve this with limited workspace, we introduce a
compact representation of planar graphs, called an -net which allows us to
manipulate its component structure during the execution of the algorithm
The Role of Consciousness in Memory
Conscious events interact with memory systems in learning, rehearsal and retrieval (Ebbinghaus 1885/1964; Tulving 1985). Here we present hypotheses that arise from the IDA computional model (Franklin, Kelemen and McCauley 1998; Franklin 2001b) of global workspace theory (Baars 1988, 2002). Our primary tool for this exploration is a flexible cognitive cycle employed by the IDA computational model and hypothesized to be a basic element of human cognitive processing. Since cognitive cycles are hypothesized to occur five to ten times a second and include interaction between conscious contents and several of the memory systems, they provide the means for an exceptionally fine-grained analysis of various cognitive tasks. We apply this tool to the small effect size of subliminal learning compared to supraliminal learning, to process dissociation, to implicit learning, to recognition vs. recall, and to the availability heuristic in recall. The IDA model elucidates the role of consciousness in the updating of perceptual memory, transient episodic memory, and procedural memory. In most cases, memory is hypothesized to interact with conscious events for its normal functioning. The methodology of the paper is unusual in that the hypotheses and explanations presented are derived from an empirically based, but broad and qualitative computational model of human cognition
Space-Time Trade-offs for Stack-Based Algorithms
In memory-constrained algorithms we have read-only access to the input, and
the number of additional variables is limited. In this paper we introduce the
compressed stack technique, a method that allows to transform algorithms whose
space bottleneck is a stack into memory-constrained algorithms. Given an
algorithm \alg\ that runs in O(n) time using variables, we can
modify it so that it runs in time using a workspace of O(s)
variables (for any ) or time using variables (for any ). We also show how the technique
can be applied to solve various geometric problems, namely computing the convex
hull of a simple polygon, a triangulation of a monotone polygon, the shortest
path between two points inside a monotone polygon, 1-dimensional pyramid
approximation of a 1-dimensional vector, and the visibility profile of a point
inside a simple polygon. Our approach exceeds or matches the best-known results
for these problems in constant-workspace models (when they exist), and gives
the first trade-off between the size of the workspace and running time. To the
best of our knowledge, this is the first general framework for obtaining
memory-constrained algorithms
A Time-Space Tradeoff for Triangulations of Points in the Plane
In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm
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