128 research outputs found
In pursuit of the dynamic optimality conjecture
In 1985, Sleator and Tarjan introduced the splay tree, a self-adjusting
binary search tree algorithm. Splay trees were conjectured to perform within a
constant factor as any offline rotation-based search tree algorithm on every
sufficiently long sequence---any binary search tree algorithm that has this
property is said to be dynamically optimal. However, currently neither splay
trees nor any other tree algorithm is known to be dynamically optimal. Here we
survey the progress that has been made in the almost thirty years since the
conjecture was first formulated, and present a binary search tree algorithm
that is dynamically optimal if any binary search tree algorithm is dynamically
optimal.Comment: Preliminary version of paper to appear in the Conference on Space
Efficient Data Structures, Streams and Algorithms to be held in August 2013
in honor of Ian Munro's 66th birthda
Unfolding Orthogonal Polyhedra with Quadratic Refinement: The Delta-Unfolding Algorithm
We show that every orthogonal polyhedron homeomorphic to a sphere can be
unfolded without overlap while using only polynomially many (orthogonal) cuts.
By contrast, the best previous such result used exponentially many cuts. More
precisely, given an orthogonal polyhedron with n vertices, the algorithm cuts
the polyhedron only where it is met by the grid of coordinate planes passing
through the vertices, together with Theta(n^2) additional coordinate planes
between every two such grid planes.Comment: 15 pages, 10 figure
Subventricular zone stem cells are heterogeneous with respect to their embryonic origins and neurogenic fates in the adult olfactory bulb
Wedetermined the embryonic origins of adult forebrain subventricular zone (SVZ) stem cells by Cre-lox fate mapping in transgenic mice. We found that all parts of the telencephalic neuroepithelium, including the medial ganglionic eminence and lateral ganglionic eminence (LGE) and the cerebral cortex, contribute multipotent, self-renewing stem cells to the adult SVZ. Descendants of the embryonic LGE and cortex settle in ventral and dorsal aspects of the dorsolateral SVZ, respectively. Both populations contribute new (5-bromo-2(')-deoxyuridine- labeled) tyrosine hydroxylase- and calretinin-positive interneurons to the adult olfactory bulb. However, calbindin-positive interneurons in the olfactory glomeruli were generated exclusively by LGE- derived stem cells. Thus, different SVZ stem cells have different embryonic origins, colonize different parts of the SVZ, and generate different neuronal progeny, suggesting that some aspects of embryonic patterning are preserved in the adult SVZ. This could have important implications for the design of endogenous stem cell-based therapies in the future
The Frequent Items Problem in Online Streaming under Various Performance Measures
In this paper, we strengthen the competitive analysis results obtained for a
fundamental online streaming problem, the Frequent Items Problem. Additionally,
we contribute with a more detailed analysis of this problem, using alternative
performance measures, supplementing the insight gained from competitive
analysis. The results also contribute to the general study of performance
measures for online algorithms. It has long been known that competitive
analysis suffers from drawbacks in certain situations, and many alternative
measures have been proposed. However, more systematic comparative studies of
performance measures have been initiated recently, and we continue this work,
using competitive analysis, relative interval analysis, and relative worst
order analysis on the Frequent Items Problem.Comment: IMADA-preprint-c
Cache-Oblivious Persistence
Partial persistence is a general transformation that takes a data structure
and allows queries to be executed on any past state of the structure. The
cache-oblivious model is the leading model of a modern multi-level memory
hierarchy.We present the first general transformation for making
cache-oblivious model data structures partially persistent
Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs
A (1 + eps)-approximate distance oracle for a graph is a data structure that
supports approximate point-to-point shortest-path-distance queries. The most
relevant measures for a distance-oracle construction are: space, query time,
and preprocessing time. There are strong distance-oracle constructions known
for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs
(Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n)
space for n-node graphs. We argue that a very low space requirement is
essential. Since modern computer architectures involve hierarchical memory
(caches, primary memory, secondary memory), a high memory requirement in effect
may greatly increase the actual running time. Moreover, we would like data
structures that can be deployed on small mobile devices, such as handhelds,
which have relatively small primary memory. In this paper, for planar graphs,
bounded-genus graphs, and minor-excluded graphs we give distance-oracle
constructions that require only O(n) space. The big O hides only a fixed
constant, independent of \epsilon and independent of genus or size of an
excluded minor. The preprocessing times for our distance oracle are also faster
than those for the previously known constructions. For planar graphs, the
preprocessing time is O(n lg^2 n). However, our constructions have slower query
times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our
linear-space results, we can in fact ensure, for any delta > 0, that the space
required is only 1 + delta times the space required just to represent the graph
itself
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Bucket Game with Applications to Set Multicover and Dynamic Page Migration
We present a simple two-person Bucket Game, based on throwing balls into buckets, and we discuss possible players’ strategies. We use these strategies to create an approximation algorithm for a generalization of the well known Set Cover problem, where we need to cover each element by at least k sets. Furthermore, we apply these strategies to construct a randomized algorithm for Dynamic Page Migration problem achieving the optimal competitive ratio against an oblivious adversary
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