674 research outputs found
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
African Americans (Research Report #121)
From the early 18th century to now, African-Americans have lived in Louisiana and the other Gulf states and played an integral role in shaping the linguistic and cultural traditions of the region. The seventh in the series discusses the experiences of African-Americans in the region.https://digitalcommons.lsu.edu/agcenter_researchreports/1006/thumbnail.jp
Global Cardinality Constraints Make Approximating Some Max-2-CSPs Harder
Assuming the Unique Games Conjecture, we show that existing approximation algorithms for some Boolean Max-2-CSPs with cardinality constraints are optimal. In particular, we prove that Max-Cut with cardinality constraints is UG-hard to approximate within ~~0.858, and that Max-2-Sat with cardinality constraints is UG-hard to approximate within ~~0.929. In both cases, the previous best hardness results were the same as the hardness of the corresponding unconstrained Max-2-CSP (~~0.878 for Max-Cut, and ~~0.940 for Max-2-Sat).
The hardness for Max-2-Sat applies to monotone Max-2-Sat instances, meaning that we also obtain tight inapproximability for the Max-k-Vertex-Cover problem
âComo refugiados en su propio paĂsâ: La formaciĂłn racial en Estados Unidos despuĂ©s del Katrina.
The controversy that followed hurricane Katrina and its representation by the media revealed unresolved racial issues in contemporary United States. Present-day New Orleans has become an ideal site for the application of Michael Omi and Howard Winantâs âracial formationâ theory, which challenges essentialist visions of race pointing to its sociohistorical construction. The present article makes use of this theoretical perspective to examine two pieces of fiction set in post-Katrina U.S.: HBOâs TV series Treme , and Richard Fordâs short-story âLeaving for Kenoshaâ. Such an analysis unveils key connections between race and class, ideology, politics or the role of the media. Keywords : Racial formation, Katrina, race, African Americans, mass media
Hardness of Approximate Nearest Neighbor Search
We prove conditional near-quadratic running time lower bounds for approximate
Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance.
Specifically, unless the Strong Exponential Time Hypothesis (SETH) is false,
for every there exists a constant such that computing a
-approximation to the Bichromatic Closest Pair requires
time. In particular, this implies a near-linear query time for
Approximate Nearest Neighbor search with polynomial preprocessing time.
Our reduction uses the Distributed PCP framework of [ARW'17], but obtains
improved efficiency using Algebraic Geometry (AG) codes. Efficient PCPs from AG
codes have been constructed in other settings before [BKKMS'16, BCGRS'17], but
our construction is the first to yield new hardness results
Biomedical Question Answering: A Survey of Approaches and Challenges
Automatic Question Answering (QA) has been successfully applied in various
domains such as search engines and chatbots. Biomedical QA (BQA), as an
emerging QA task, enables innovative applications to effectively perceive,
access and understand complex biomedical knowledge. There have been tremendous
developments of BQA in the past two decades, which we classify into 5
distinctive approaches: classic, information retrieval, machine reading
comprehension, knowledge base and question entailment approaches. In this
survey, we introduce available datasets and representative methods of each BQA
approach in detail. Despite the developments, BQA systems are still immature
and rarely used in real-life settings. We identify and characterize several key
challenges in BQA that might lead to this issue, and discuss some potential
future directions to explore.Comment: In submission to ACM Computing Survey
Random input helps searching predecessors
A data structure problem consists of the finite sets: D of data, Q of queries, A of query answers, associated with a function f: D x Q â A. The data structure of file X is "static" ("dynamic") if we "do not" ("do") require quick updates as X changes. An important goal is to compactly encode a file X Ï” D, such that for each query y Ï” Q, function f (X, y) requires the minimum time to compute an answer in A. This goal is trivial if the size of D is large, since for each query y Ï” Q, it was shown that f(X,y) requires O(1) time for the most important queries in the literature. Hence, this goal becomes interesting to study as a trade off between the "storage space" and the "query time", both measured as functions of the file size n = \X\. The ideal solution would be to use linear O(n) = O(\X\) space, while retaining a constant O(1) query time. However, if f (X, y) computes the static predecessor search (find largest x Ï” X: x †y), then Ajtai [Ajt88] proved a negative result. By using just n0(1) = [IX]0(1) data space, then it is not possible to evaluate f(X,y) in O(1) time Ay Ï” Q. The proof exhibited a bad distribution of data D, such that Eyâ Ï” Q (a "difficult" query yâ), that f(X,yâ) requires Ï(1) time. Essentially [Ajt88] is an existential result, resolving the worst case scenario. But, [Ajt88] left open the question: do we typically, that is, with high probability (w.h.p.)1 encounter such "difficult" queries y Ï” Q, when assuming reasonable distributions with respect to (w.r.t.) queries and data? Below we make reasonable assumptions w.r.t. the distribution of the queries y Ï” Q, as well as w.r.t. the distribution of data X Ï” D. In two interesting scenarios studied in the literature, we resolve the typical (w.h.p.) query time
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