1,651 research outputs found
Frames, Graphs and Erasures
Two-uniform frames and their use for the coding of vectors are the main
subject of this paper. These frames are known to be optimal for handling up to
two erasures, in the sense that they minimize the largest possible error when
up to two frame coefficients are set to zero. Here, we consider various
numerical measures for the reconstruction error associated with a frame when an
arbitrary number of the frame coefficients of a vector are lost. We derive
general error bounds for two-uniform frames when more than two erasures occur
and apply these to concrete examples. We show that among the 227 known
equivalence classes of two-uniform (36,15)-frames arising from Hadamard
matrices, there are 5 that give smallest error bounds for up to 8 erasures.Comment: 28 pages LaTeX, with AMS macros; v.3: fixed Thm 3.6, added comment,
Lemma 3.7 and Proposition 3.8, to appear in Lin. Alg. App
Diversifying Top-K Results
Top-k query processing finds a list of k results that have largest scores
w.r.t the user given query, with the assumption that all the k results are
independent to each other. In practice, some of the top-k results returned can
be very similar to each other. As a result some of the top-k results returned
are redundant. In the literature, diversified top-k search has been studied to
return k results that take both score and diversity into consideration. Most
existing solutions on diversified top-k search assume that scores of all the
search results are given, and some works solve the diversity problem on a
specific problem and can hardly be extended to general cases. In this paper, we
study the diversified top-k search problem. We define a general diversified
top-k search problem that only considers the similarity of the search results
themselves. We propose a framework, such that most existing solutions for top-k
query processing can be extended easily to handle diversified top-k search, by
simply applying three new functions, a sufficient stop condition sufficient(),
a necessary stop condition necessary(), and an algorithm for diversified top-k
search on the current set of generated results, div-search-current(). We
propose three new algorithms, namely, div-astar, div-dp, and div-cut to solve
the div-search-current() problem. div-astar is an A* based algorithm, div-dp is
an algorithm that decomposes the results into components which are searched
using div-astar independently and combined using dynamic programming. div-cut
further decomposes the current set of generated results using cut points and
combines the results using sophisticated operations. We conducted extensive
performance studies using two real datasets, enwiki and reuters. Our div-cut
algorithm finds the optimal solution for diversified top-k search problem in
seconds even for k as large as 2,000.Comment: VLDB201
Fixed-Parameter Algorithms for Rectilinear Steiner tree and Rectilinear Traveling Salesman Problem in the plane
Given a set of points with their pairwise distances, the traveling
salesman problem (TSP) asks for a shortest tour that visits each point exactly
once. A TSP instance is rectilinear when the points lie in the plane and the
distance considered between two points is the distance. In this paper, a
fixed-parameter algorithm for the Rectilinear TSP is presented and relies on
techniques for solving TSP on bounded-treewidth graphs. It proves that the
problem can be solved in where denotes the
number of horizontal lines containing the points of . The same technique can
be directly applied to the problem of finding a shortest rectilinear Steiner
tree that interconnects the points of providing a
time complexity. Both bounds improve over the best time bounds known for these
problems.Comment: 24 pages, 13 figures, 6 table
Truss Decomposition in Massive Networks
The k-truss is a type of cohesive subgraphs proposed recently for the study
of networks. While the problem of computing most cohesive subgraphs is NP-hard,
there exists a polynomial time algorithm for computing k-truss. Compared with
k-core which is also efficient to compute, k-truss represents the "core" of a
k-core that keeps the key information of, while filtering out less important
information from, the k-core. However, existing algorithms for computing
k-truss are inefficient for handling today's massive networks. We first improve
the existing in-memory algorithm for computing k-truss in networks of moderate
size. Then, we propose two I/O-efficient algorithms to handle massive networks
that cannot fit in main memory. Our experiments on real datasets verify the
efficiency of our algorithms and the value of k-truss.Comment: VLDB201
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