18,732 research outputs found
A Symbolic Computational Approach to a Problem Involving Multivariate Poisson Distributions
Multivariate Poisson random variables subject to linear integer constraints
arise in several application areas, such as queuing and biomolecular networks.
This note shows how to compute conditional statistics in this context, by
employing WF Theory and associated algorithms. A symbolic computation package
has been developed and is made freely available. A discussion of motivating
biomolecular problems is also provided.Comment: 19 pages, accompanied by a maple package MVPoisson downloadable from
http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/mvp.htm
On Balanced k-coverage in Visual Sensor Network
Given a set of directional visual sensors, the -coverage problem
determines the orientation of minimal directional sensors so that each target
is covered at least times. As the problem is NP-complete, a number of
heuristics have been devised to tackle the issue. However, the existing
heuristics provide imbalance coverage of the targets--some targets are covered
times while others are left totally uncovered or singly covered. The
coverage imbalance is more serious in under-provisioned networks where there do
not exist enough sensors to cover all the targets times. Therefore, we
address the problem of covering each target at least times in a balanced
way using minimum number of sensors. We study the existing Integer Linear
Programming (ILP) formulation for single coverage and extend the idea for
-coverage. However, the extension does not balance the coverage of the
targets. We further propose Integer Quadratic Programming (IQP) and Integer
Non-Linear Programming (INLP) formulations that are capable of addressing the
coverage balancing. As the proposed formulations are computationally expensive,
we devise a faster Centralized Greedy -Coverage Algorithm (CGkCA) to
approximate the formulations. Finally, through rigorous simulation experiments
we show the efficacy of the proposed formulations and the CGkCA
Computing the Line Index of Balance Using Integer Programming Optimisation
An important measure of signed graphs is the line index of balance which has
several applications in many fields. However, this graph-theoretic measure was
underused for decades because of the inherent complexity in its computation
which is closely related to solving NP-hard graph optimisation problems like
MAXCUT. We develop new quadratic and linear programming models to compute the
line index of balance exactly. Using the Gurobi integer programming
optimisation solver, we evaluate the line index of balance on real-world and
synthetic datasets. The synthetic data involves Erd\H{o}s-R\'{e}nyi graphs,
Barab\'{a}si-Albert graphs, and specially structured random graphs. We also use
well known datasets from the sociology literature, such as signed graphs
inferred from students' choice and rejection as well as datasets from the
biology literature including gene regulatory networks. The results show that
exact values of the line index of balance in relatively large signed graphs can
be efficiently computed using our suggested optimisation models. We find that
most real-world social networks and some biological networks have small line
index of balance which indicates that they are close to balanced.Comment: Accepted author copy, 20 pages, 4 tables and 3 figures. This work is
followed up in another study with more focus on Operations Research aspects
of the topic that can be found in arXiv:1611.0903
Structured Projection-Based Model Reduction with Application to Stochastic Biochemical Networks
The Chemical Master Equation (CME) is well known to provide the highest
resolution models of a biochemical reaction network. Unfortunately, even
simulating the CME can be a challenging task. For this reason more simple
approximations to the CME have been proposed. In this work we focus on one such
model, the Linear Noise Approximation. Specifically, we consider implications
of a recently proposed LNA time-scale separation method. We show that the
reduced order LNA converges to the full order model in the mean square sense.
Using this as motivation we derive a network structure preserving reduction
algorithm based on structured projections. We present convex optimisation
algorithms that describe how such projections can be computed and we discuss
when structured solutions exits. We also show that for a certain class of
systems, structured projections can be found using basic linear algebra and no
optimisation is necessary. The algorithms are then applied to a linearised
stochastic LNA model of the yeast glycolysis pathway.Comment: 13 pages; 7 figures; submitted to IEEE Transaction on Automatic
Contro
Towards balanced clustering - part 1 (preliminaries)
The article contains a preliminary glance at balanced clustering problems.
Basic balanced structures and combinatorial balanced problems are briefly
described. A special attention is targeted to various balance/unbalance indices
(including some new versions of the indices): by cluster cardinality, by
cluster weights, by inter-cluster edge/arc weights, by cluster element
structure (for element multi-type clustering). Further, versions of
optimization clustering problems are suggested (including multicriteria problem
formulations). Illustrative numerical examples describe calculation of balance
indices and element multi-type balance clustering problems (including example
for design of student teams).Comment: 21 pages, 17 figures, 14 table
mplrs: A scalable parallel vertex/facet enumeration code
We describe a new parallel implementation, mplrs, of the vertex enumeration
code lrs that uses the MPI parallel environment and can be run on a network of
computers. The implementation makes use of a C wrapper that essentially uses
the existing lrs code with only minor modifications. mplrs was derived from the
earlier parallel implementation plrs, written by G. Roumanis in C++. plrs uses
the Boost library and runs on a shared memory machine. In developing mplrs we
discovered a method of balancing the parallel tree search, called budgeting,
that greatly improves parallelization beyond the bottleneck encountered
previously at around 32 cores.
This method can be readily adapted for use in other reverse search
enumeration codes. We also report some preliminary computational results
comparing parallel and sequential codes for vertex/facet enumeration problems
for convex polyhedra. The problems chosen span the range from simple to highly
degenerate polytopes. For most problems tested, the results clearly show the
advantage of using the parallel implementation mplrs of the reverse search
based code lrs, even when as few as 8 cores are available. For some problems
almost linear speedup was observed up to 1200 cores, the largest number of
cores tested.Comment: Revision incorporating additional suggested change
Load Balancing in Mobility-on-Demand Systems: Reallocation Via Parametric Control Using Concurrent Estimation
Mobility-on-Demand (MoD) systems require load balancing to maintain
consistent service across regions with uneven demand subject to time-varying
traffic conditions. The load-balancing objective is to jointly minimize the
fraction of lost customer requests due to vehicle unavailability and the
fraction of time when vehicles drive empty during load balancing operations. In
order to bypass the intractability of a globally optimal solution to this
stochastic dynamic optimization problem, we propose a parametric
threshold-based control driven by the known relative abundance of vehicles
available in and en route to each region. This is still a difficult parametric
optimization problem for which one often resorts to trial-and-error methods
where multiple sample paths are generated through simulation or from actual
data under different parameter settings. In contrast, this paper utilizes
concurrent estimation methods to simultaneously construct many sample paths
from a single nominal sample path. The performance of the parametric controller
for intermediate size systems is compared to that of a simpler single-parameter
controller, a state-blind static controller, a policy of no control, and a
theoretically-derived lower bound. Simulation results show the value of state
information in improving performance
Multi-Dimensional Balanced Graph Partitioning via Projected Gradient Descent
Motivated by performance optimization of large-scale graph processing systems
that distribute the graph across multiple machines, we consider the balanced
graph partitioning problem. Compared to the previous work, we study the
multi-dimensional variant when balance according to multiple weight functions
is required. As we demonstrate by experimental evaluation, such
multi-dimensional balance is important for achieving performance improvements
for typical distributed graph processing workloads. We propose a new scalable
technique for the multidimensional balanced graph partitioning problem. The
method is based on applying randomized projected gradient descent to a
non-convex continuous relaxation of the objective. We show how to implement the
new algorithm efficiently in both theory and practice utilizing various
approaches for projection. Experiments with large-scale social networks
containing up to hundreds of billions of edges indicate that our algorithm has
superior performance compared with the state-of-the-art approaches
Data-Driven Robust Taxi Dispatch under Demand Uncertainties
In modern taxi networks, large amounts of taxi occupancy status and location
data are collected from networked in-vehicle sensors in real-time. They provide
knowledge of system models on passenger demand and mobility patterns for
efficient taxi dispatch and coordination strategies. Such approaches face new
challenges: how to deal with uncertainties of predicted customer demand while
fulfilling the system's performance requirements, including minimizing taxis'
total idle mileage and maintaining service fairness across the whole city; how
to formulate a computationally tractable problem. To address this problem, we
develop a data-driven robust taxi dispatch framework to consider
spatial-temporally correlated demand uncertainties. The robust vehicle dispatch
problem we formulate is concave in the uncertain demand and convex in the
decision variables. Uncertainty sets of random demand vectors are constructed
from data based on theories in hypothesis testing, and provide a desired
probabilistic guarantee level for the performance of robust taxi dispatch
solutions. We prove equivalent computationally tractable forms of the robust
dispatch problem using the minimax theorem and strong duality. Evaluations on
four years of taxi trip data for New York City show that by selecting a
probabilistic guarantee level at 75%, the average demand-supply ratio error is
reduced by 31.7%, and the average total idle driving distance is reduced by
10.13% or about 20 million miles annually, compared with non-robust dispatch
solutions.Comment: Accepted as a regular paper, IEEE Transactions on Control Systems
Technology; 15 pages. This version updated as of Oct 201
Characterization of SINR Region for Multiple Interfering Multicast in Power-Controlled Systems
This paper considers a wireless communication network consisting of multiple
interfering multicast sessions. Different from a unicast system where each
transmitter has only one receiver, in a multicast system, each transmitter has
multiple receivers. It is a well known result for wireless unicast systems that
the feasibility of an signal-to-interference-plus-noise power ratio (SINR)
without power constraint is decided by the Perron-Frobenius eigenvalue of a
nonnegative matrix. We generalize this result and propose necessary and
sufficient conditions for the feasibility of an SINR in a wireless multicast
system with and without power constraint. The feasible SINR region as well as
its geometric properties are studied. Besides, an iterative algorithm is
proposed which can efficiently check the feasibility condition and compute the
boundary points of the feasible SINR region.Comment: 25 pages, 4 figures, submitted to IEEE Trans. Inform. Theor
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