Research Projects and Publications
Many projects are listed below, some from the past and some I'm pursuing now in group sizes varying from one to a dozen.
Collaboration is welcomed, or you might suggest new projects.
Research projects for students: you should read this if you are interested in working with me.
Research areas are organized as follows:
Here is a listing of my
books, papers, etc.,
organized by research area, and here is a standard
Our work in parallel computing has involved developing efficient
algorithms for large problems in computational science and engineering,
and more theoretical algorithms for a variety of problems and
Other work has involved understanding and improving the
performance of parallel systems, and proposing new
Most of the work on using large machines involves the research
mentioned in scientific
computing and computational science and some of that described
in adaptive sampling.
Research involving more theoretical algorithms includes algorithms for
graph theory, geometry, image processing, sorting,
routing, and message-passing.
Russ Miller and I wrote
Parallel Algorithms for Regular Architectures: Meshes and Pyramids
which has many algorithms
for these machines.
Some of the papers we've written for various machine models are
For fundamental problems such as sorting, finding a minimal spanning tree, etc., all of the above models are faster than quantum computers.
Few people are aware that while quantum is extremely good for factoring, for many other problems it is slower than classical mechanics.
Some projects I'm involved with, or would like to start:
The parallel computing topics I'm interested often change, and, as I said,
I'm interested in collaboration and new problems.
I'm particularly interested in problems where being able to exploit
a very large number of processors helps one solve problems that
otherwise are impossible to solve in a useful amount of time.
Here is a somewhat whimsical explanation of
In standard clinical trials, one may
allocate equal numbers of patients to one of two treatments, and then
after all of the outcomes have been observed make a statistical decision
as to which is the better treatment. With an adaptive design, however,
one may modify the allocation as the outcomes are being observed, so
that more patients in the trial can be allocated to the better treatment.
This can simultaneously allow one to achieve a desired statistical goal
(such as determining which is the better treatment) while also achieving
ethical or cost goals (such as reducing patient suffering during the trial,
or reducing costs in an industrial setting).
Adaptive designs have many natural uses in resource allocation problems or choosing parameter settings
for computer simulations, since the computer can both collect the information
and run a program to decide what to do next.
They can be viewed as a dynamic learning process, and there are numerous
ties to optimization.
Here is a more extensive discussion of adaptive sampling and bandit problems.
Here the emphasis is on developing efficient
algorithms and data structures that are motivated by needs
in computational science, and on ways of putting large scientific codes
Most of my work in this area started with a scientist coming to me requesting
help on a research project. I've worked with social scientists,
environmental engineers, space scientists, statisticians, etc.
Some of the scientists are internationally famous, while others are
graduate students just starting to explore a topic.
I married one of these scientists - you never know where exciting
research will lead.
For adaptive sampling I'm involved in both the
science and the computing, while within the
Center for Space Environment Modeling (CSEM)
and Center For Radiative Shock Hydrodynamics (CRASH)
I concentrate on the computer science aspects.
CRASH is a Dept. of Energy Center of Excellence in Predictive
Science, where we are focusing not just on predicting the results of an
experiment, but also quantifying the uncertainty of our predictions,
and why we think we know the uncertainty.
``Uncertainty quantification'' is a research area which is
attracting a lot of attention.
Because several of these applications involve large problems, much
of our work in this area
involves parallel computing, including some
of the largest supercomputers in the world, though some
involves serial algorithms.
- Adaptive blocks: a scalable parallel
data structure used for adaptive mesh refinement.
Bob Oehmke developed a spherical version
that is being used in atmospheric and space environment modeling
codes, while a cartesian version is
being used for the major codes in CSEM and CRASH.
- Software frameworks: we created the
Space Weather Modeling Framework
for merging large scientific
codes running on parallel machines into an efficient complex simulation
of the Sun to Earth space environment.
This is being used by NASA and the Air Force Space Command for
space weather prediction.
I'm also on the executive committee of the
Earth Systems Modeling
Framework, which is being used by several groups, including the
daily national weather predictions by NOAA.
- Load balancing:
Andy Poe and I developed a new approach for balancing
geometrically based problems where there
are two aspects that need to be balanced.
This improved the efficiency of a parallel program
for car crash simulation.
The algorithm is based on the Ham Sandwich theorem from algebraic
topology. We've also used space-filling curves for geometric data.
- Efficient parallel algorithms using dynamic programming:
for optimizing and evaluating modeling some of the complex situations
we encounter in the adaptive sampling work.
For example, we were able to optimize a
clinical trial with 200 patients
and three treatment alternatives.
This had previously been considered to be infeasible.
This paper, with Bob Oehmke and Janis Hardwick, was finalist for best
paper at the Supercomputing conference.
A related research question is how
to automatically turn recursive equations into efficient serial and parallel
programs. Denny Vandenberg has worked on this.
Most of the work here concentrates on trying to develop optimal
algorithms, optimal at least as measured by O-notation.
The majority of my work on algorithms has been in
adaptive allocation, or
graph theory, but there are several other
topics that my students or collaborators and I have looked at.
Some of the work we did involves
- Balancing binary search trees,
requiring only linear time and constant space. This was with
- Computing the
Busy Beaver function, with Rona Kopp.
We computed the largest value known. It can be proven that there is a natural number such that the busy beaver cannot be computed for that number or any larger one, but no one knows what that number is.
- Sublogarithmic algorithms for PRAMs,
solving problems in geometry and graph theory, and proving lower
bounds for them. One interesting aspect is that
we were able to solve some problems faster than a PRAM can count.
Phil MacKenzie won the university Best Thesis award for this work.
- Reiko Tanese and Ted Belding studied an ``island'' model of
genetic algorithms where there are evolving
subpopulations, with occasional migration between islands. This is
better than classical GA approaches. This started as a term project
in my parallel computing class, and then we noticed that the behavior wasn't
what we expected. Trying to figure out what was happening led to Reiko's
Some projects I'm currently involved with, or would like to start
(in addition to the topics listed in parallel computing)
- Algorithms for random data:
Suppose you know that points are chosen from some 2-dimensional distribution,
but you don't know what the distribution is. How fast (in expected time)
can you find the convex hull of a set of n points, for either serial
or parallel computers?
Phil MacKenzie and I worked on
algorithms for PRAMs when the distribution was known,
and Doug Van Wieren worked on related
algorithms for a reconfigurable mesh.
- Isotonic and unimodal regression
algorithms, and more general shape-constrained nonparametric regression.
E.g., given data, you might want to predict weight as a function of height
and shirt size.
Suppose you are only willing to assume that the weight increases with
height, and with shirt size, so you want to find the best regression that
has no restrictions other than these.
Standard linear regression makes no sense on ordered sets such as shirt
Many questions about resource allocation, fault tolerance,
routing, scheduling, synchronization,
etc., for distributed memory machines can be modeled via graphs, and one
can exploit the graph structure to find solutions.
We have particularly emphasized hypercube, mesh, and torus models, since many
parallel computers are of this form.
Example of this work are a rather comprehensive paper on the subcube
of the hypercube and one on
embedding graphs into hypercubes.
One set of graph theory questions Marilynn Livingston and I
pursued concerns the determination
of various properties of families such as k x n meshes,
with k fixed.
We have shown that values such as domination numbers, packing numbers,
number of code words, number of tilings, etc., can be
determined in closed form, using
properties of finite state automata.
This was a rather dramatic improvement upon earlier results.
There are several interesting
questions and conjectures related to this.
The work with Julia Lipman mentioned above, concerning repeated
synchronization of multiple agents, is also research in discrete
I don't work in this area any more.
Most of the work in operator theory concerned Schur multiplication of
matrices, where the Schur product is formed by multiplying matrices
termwise (much as addition is performed).
For infinite dimensional
this forms an
interesting Banach algebra, which has a many ties to normal
Investigating the Schur product led to questions about the
range and majorization of diagonal entries.
Slightly related results concerned determining the numerical range of
One paper analyzed conditionally convergent series and
There is a natural duality between sets of
conditionally convergent series and sets of permutations which leave their
sums unchanged, and this duality has some unusual properties.
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