1,241 research outputs found
On Distributed Computation in Noisy Random Planar Networks
We consider distributed computation of functions of distributed data in
random planar networks with noisy wireless links. We present a new algorithm
for computation of the maximum value which is order optimal in the number of
transmissions and computation time.We also adapt the histogram computation
algorithm of Ying et al to make the histogram computation time optimal.Comment: 5 pages, 2 figure
Limit laws for k-coverage of paths by a Markov-Poisson-Boolean model
Let P := {X_i,i >= 1} be a stationary Poisson point process in R^d, {C_i,i >=
1} be a sequence of i.i.d. random sets in R^d, and {Y_i^t; t \geq 0, i >= 1} be
i.i.d. {0,1}-valued continuous time stationary Markov chains. We define the
Markov-Poisson-Boolean model C_t := {Y_i^t(X_i + C_i), i >= 1}. C_t represents
the coverage process at time t. We first obtain limit laws for k-coverage of an
area at an arbitrary instant. We then obtain the limit laws for the k-coverage
seen by a particle as it moves along a one-dimensional path.Comment: 1 figure. 24 Pages. Accepted at Stochastic Models. Theorems 6 and 7
corrected. Theorem 9 and Appendix adde
Optimal Embedding of Functions for In-Network Computation: Complexity Analysis and Algorithms
We consider optimal distributed computation of a given function of
distributed data. The input (data) nodes and the sink node that receives the
function form a connected network that is described by an undirected weighted
network graph. The algorithm to compute the given function is described by a
weighted directed acyclic graph and is called the computation graph. An
embedding defines the computation communication sequence that obtains the
function at the sink. Two kinds of optimal embeddings are sought, the embedding
that---(1)~minimizes delay in obtaining function at sink, and (2)~minimizes
cost of one instance of computation of function. This abstraction is motivated
by three applications---in-network computation over sensor networks, operator
placement in distributed databases, and module placement in distributed
computing.
We first show that obtaining minimum-delay and minimum-cost embeddings are
both NP-complete problems and that cost minimization is actually MAX SNP-hard.
Next, we consider specific forms of the computation graph for which polynomial
time solutions are possible. When the computation graph is a tree, a polynomial
time algorithm to obtain the minimum delay embedding is described. Next, for
the case when the function is described by a layered graph we describe an
algorithm that obtains the minimum cost embedding in polynomial time. This
algorithm can also be used to obtain an approximation for delay minimization.
We then consider bounded treewidth computation graphs and give an algorithm to
obtain the minimum cost embedding in polynomial time
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