The Discrete Pulse Transform (DPT) makes use of LULU
smoothing to decompose a signal into block pulses. The most recent and
effective implementation of the DPT is an algorithm called the Roadmaker's Pavage, which uses a graph-based algorithm that produces a hierarchical tree of pulses as its final output. This algorithm has been
shown to have important applications in articial intelligence and pattern recognition. Even though the Roadmakerfo's Pavage is an efficient
implementation, the theoretical structure of the DPT results in a slow,
deterministic algorithm. This paper examines the use of the spectral
domain of graphs and designing graph filter banks to downsample the
Roadmaker's Pavage algorithm. We investigate the extent to which this
speeds up the algorithm and allows parallel processing. Converting graph
signals to the spectral domain can also be a costly overhead, and so methods of estimation for filter banks are examined, as well as the design of
a good filter bank that may be reused without needing recalculation.
Rado constructed a (simple) denumerable graph R with the positive integers
as vertex set with the following edges: for given m and n with m < n, m is
adjacent to n if n has a 1 in the mth position of its binary expansion. ...
Rado constructed a (simple) denumerable graph R with the positive integers as vertex set
with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in
the m'th position of its binary expansion. ...
We extend results about asymmetric colorings of finite Cartesian products of graphs to strong and direct products of graphs and digraphs. On the way we shorten proofs for the existence of prime factorizations of finite ...