18 research outputs found
Drift rate control of a Brownian processing system
A system manager dynamically controls a diffusion process Z that lives in a
finite interval [0,b]. Control takes the form of a negative drift rate \theta
that is chosen from a fixed set A of available values. The controlled process
evolves according to the differential relationship dZ=dX-\theta(Z) dt+dL-dU,
where X is a (0,\sigma) Brownian motion, and L and U are increasing processes
that enforce a lower reflecting barrier at Z=0 and an upper reflecting barrier
at Z=b, respectively. The cumulative cost process increases according to the
differential relationship d\xi =c(\theta(Z)) dt+p dU, where c(\cdot) is a
nondecreasing cost of control and p>0 is a penalty rate associated with
displacement at the upper boundary. The objective is to minimize long-run
average cost. This problem is solved explicitly, which allows one to also solve
the following, essentially equivalent formulation: minimize the long-run
average cost of control subject to an upper bound constraint on the average
rate at which U increases. The two special problem features that allow an
explicit solution are the use of a long-run average cost criterion, as opposed
to a discounted cost criterion, and the lack of state-related costs other than
boundary displacement penalties. The application of this theory to power
control in wireless communication is discussed.Comment: Published at http://dx.doi.org/10.1214/105051604000000855 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
FLEET: Butterfly Estimation from a Bipartite Graph Stream
We consider space-efficient single-pass estimation of the number of
butterflies, a fundamental bipartite graph motif, from a massive bipartite
graph stream where each edge represents a connection between entities in two
different partitions. We present a space lower bound for any streaming
algorithm that can estimate the number of butterflies accurately, as well as
FLEET, a suite of algorithms for accurately estimating the number of
butterflies in the graph stream. Estimates returned by the algorithms come with
provable guarantees on the approximation error, and experiments show good
tradeoffs between the space used and the accuracy of approximation. We also
present space-efficient algorithms for estimating the number of butterflies
within a sliding window of the most recent elements in the stream. While there
is a significant body of work on counting subgraphs such as triangles in a
unipartite graph stream, our work seems to be one of the few to tackle the case
of bipartite graph streams.Comment: This is the author's version of the work. It is posted here by
permission of ACM for your personal use. Not for redistribution. The
definitive version was published in Seyed-Vahid Sanei-Mehri, Yu Zhang, Ahmet
Erdem Sariyuce and Srikanta Tirthapura. "FLEET: Butterfly Estimation from a
Bipartite Graph Stream". The 28th ACM International Conference on Information
and Knowledge Managemen