39,253 research outputs found
Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time
We present the first almost-linear time algorithm for constructing
linear-sized spectral sparsification for graphs. This improves all previous
constructions of linear-sized spectral sparsification, which requires
time.
A key ingredient in our algorithm is a novel combination of two techniques
used in literature for constructing spectral sparsification: Random sampling by
effective resistance, and adaptive constructions based on barrier functions.Comment: 22 pages. A preliminary version of this paper is to appear in
proceedings of the 56th Annual IEEE Symposium on Foundations of Computer
Science (FOCS 2015
An SDP-Based Algorithm for Linear-Sized Spectral Sparsification
For any undirected and weighted graph with vertices and
edges, we call a sparse subgraph of , with proper reweighting of the
edges, a -spectral sparsifier if holds for any , where and
are the respective Laplacian matrices of and . Noticing that
time is needed for any algorithm to construct a spectral sparsifier and a
spectral sparsifier of requires edges, a natural question is to
investigate, for any constant , if a -spectral
sparsifier of with edges can be constructed in time,
where the notation suppresses polylogarithmic factors. All previous
constructions on spectral sparsification require either super-linear number of
edges or time.
In this work we answer this question affirmatively by presenting an algorithm
that, for any undirected graph and , outputs a
-spectral sparsifier of with edges in
time. Our algorithm is based on three novel
techniques: (1) a new potential function which is much easier to compute yet
has similar guarantees as the potential functions used in previous references;
(2) an efficient reduction from a two-sided spectral sparsifier to a one-sided
spectral sparsifier; (3) constructing a one-sided spectral sparsifier by a
semi-definite program.Comment: To appear at STOC'1
Optimal Power Allocation for Two-Way Decode-and-Forward OFDM Relay Networks
This paper presents a novel two-way decode-and-forward (DF) relay strategy
for Orthogonal Frequency Division Multiplexing (OFDM) relay networks. This DF
relay strategy employs multi-subcarrier joint channel coding to leverage
frequency selective fading, and thus can achieve a higher data rate than the
conventional per-subcarrier DF relay strategies. We further propose a
low-complexity, optimal power allocation strategy to maximize the data rate of
the proposed relay strategy. Simulation results suggest that our strategy
obtains a substantial gain over the per-subcarrier DF relay strategies, and
also outperforms the amplify-and-forward (AF) relay strategy in a wide
signal-to-noise-ratio (SNR) region.Comment: 5 pages, 2 figures, accepted by IEEE ICC 201
Corrections to "Unified Laguerre polynomial-series-based distribution of small-scale fading envelopes''
In this correspondence, we point out two typographical errors in Chai and
Tjhung's paper and we offer the correct formula of the unified Laguerre
polynomial-series-based cumulative distribution function (cdf) for small-scale
fading distributions. A Laguerre polynomial-series-based cdf formula for
non-central chi-square distribution is also provided as a special case of our
unified cdf result.Comment: 2 pages, to be published in the IEEE Transactions on Vehicular
Technology as a Correspondenc
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