7,426 research outputs found
Partially-Distributed Resource Allocation in Small-Cell Networks
We propose a four-stage hierarchical resource allocation scheme for the
downlink of a large-scale small-cell network in the context of orthogonal
frequency-division multiple access (OFDMA). Since interference limits the
capabilities of such networks, resource allocation and interference management
are crucial. However, obtaining the globally optimum resource allocation is
exponentially complex and mathematically intractable. Here, we develop a
partially decentralized algorithm to obtain an effective solution. The three
major advantages of our work are: 1) as opposed to a fixed resource allocation,
we consider load demand at each access point (AP) when allocating spectrum; 2)
to prevent overloaded APs, our scheme is dynamic in the sense that as the users
move from one AP to the other, so do the allocated resources, if necessary, and
such considerations generally result in huge computational complexity, which
brings us to the third advantage: 3) we tackle complexity by introducing a
hierarchical scheme comprising four phases: user association, load estimation,
interference management via graph coloring, and scheduling. We provide
mathematical analysis for the first three steps modeling the user and AP
locations as Poisson point processes. Finally, we provide results of numerical
simulations to illustrate the efficacy of our scheme.Comment: Accepted on May 15, 2014 for publication in the IEEE Transactions on
Wireless Communication
Quasiconvex Programming
We define quasiconvex programming, a form of generalized linear programming
in which one seeks the point minimizing the pointwise maximum of a collection
of quasiconvex functions. We survey algorithms for solving quasiconvex programs
either numerically or via generalizations of the dual simplex method from
linear programming, and describe varied applications of this geometric
optimization technique in meshing, scientific computation, information
visualization, automated algorithm analysis, and robust statistics.Comment: 33 pages, 14 figure
Grid Representations and the Chromatic Number
A grid drawing of a graph maps vertices to grid points and edges to line
segments that avoid grid points representing other vertices. We show that there
is a number of grid points that some line segment of an arbitrary grid drawing
must intersect. This number is closely connected to the chromatic number.
Second, we study how many columns we need to draw a graph in the grid,
introducing some new \NP-complete problems. Finally, we show that any planar
graph has a planar grid drawing where every line segment contains exactly two
grid points. This result proves conjectures asked by David Flores-Pe\~naloza
and Francisco Javier Zaragoza Martinez.Comment: 22 pages, 8 figure
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