19,658 research outputs found
Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain
We study the computation of the diameter and radius under the rectilinear
link distance within a rectilinear polygonal domain of vertices and
holes. We introduce a \emph{graph of oriented distances} to encode the distance
between pairs of points of the domain. This helps us transform the problem so
that we can search through the candidates more efficiently. Our algorithm
computes both the diameter and the radius in time, where denotes the matrix
multiplication exponent and is the number of
edges of the graph of oriented distances. We also provide a faster algorithm
for computing the diameter that runs in time
Improved Successive Cancellation Decoding of Polar Codes
As improved versions of successive cancellation (SC) decoding algorithm,
successive cancellation list (SCL) decoding and successive cancellation stack
(SCS) decoding are used to improve the finite-length performance of polar
codes. Unified descriptions of SC, SCL and SCS decoding algorithms are given as
path searching procedures on the code tree of polar codes. Combining the ideas
of SCL and SCS, a new decoding algorithm named successive cancellation hybrid
(SCH) is proposed, which can achieve a better trade-off between computational
complexity and space complexity. Further, to reduce the complexity, a pruning
technique is proposed to avoid unnecessary path searching operations.
Performance and complexity analysis based on simulations show that, with proper
configurations, all the three improved successive cancellation (ISC) decoding
algorithms can have a performance very close to that of maximum-likelihood (ML)
decoding with acceptable complexity. Moreover, with the help of the proposed
pruning technique, the complexities of ISC decoders can be very close to that
of SC decoder in the moderate and high signal-to-noise ratio (SNR) regime.Comment: This paper is modified and submitted to IEEE Transactions on
Communication
Fast Shortest Path Distance Estimation in Large Networks
We study the problem of preprocessing a large graph so that point-to-point shortest-path queries can be answered very fast. Computing shortest paths is a well studied problem, but exact algorithms do not scale to huge graphs encountered on the web, social networks, and other applications.
In this paper we focus on approximate methods for distance estimation, in particular using landmark-based distance indexing. This approach involves selecting a subset of nodes as landmarks and computing (offline) the distances from each node in the graph to those landmarks. At runtime, when the distance between a pair of nodes is needed, we can estimate it quickly by combining the precomputed distances of the two nodes to the landmarks.
We prove that selecting the optimal set of landmarks is an NP-hard problem, and thus heuristic solutions need to be employed. Given a budget of memory for the index, which translates directly into a budget of landmarks, different landmark selection strategies can yield dramatically different results in terms of accuracy. A number of simple methods that scale well to large graphs are therefore developed and experimentally compared. The simplest methods choose central nodes of the graph, while the more elaborate ones select central nodes that are also far away from one another. The efficiency of the suggested techniques is tested experimentally using five different real world graphs with millions of edges; for a given accuracy, they require as much as 250 times less space than the current approach in the literature which considers selecting landmarks at random.
Finally, we study applications of our method in two problems arising naturally in large-scale networks, namely, social search and community detection.Yahoo! Research (internship
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