Efficient parallel route-planning methods and
rerouting to circumvent restrictions
Lab
Contact: Dr
Timothy G. Griffin
Supervisors: Dr
Jagdish J. Modi
Special Resources: None
This should appeal to students interested in the
design of parallel algorithms, but does not assume any previous parallel
computing expertise.
In the past students have considered rail networks,
both underground and overground, minimizing a single parameter such as distance
or time, and found an algorithm analogous to matrix multiplication to be
suitable for parallel computation [1].
A number of different approaches can be utilised
for parallel computation. For example, a modified form of matrix multiplication
can be used, in which we find the minimum of a sum of weights (route-lengths),
instead of forming a sum of products. By repeatedly ‘multiplying’ the route
matrix with itself, we can find the lengths of the shortest paths between all pairs
of destinations. Since matrix multiplication is a highly parallel operation,
this method is well suited to parallel computation.
The aim of the project is to implement such an
algorithm, applying to a dataset of your choice, for example, the California
road network [2]. The implementation should also include improvements to the
efficiency of computation by avoiding large sparse areas in order to minimise
data movements. The Cannon or Fox-Otto algorithms [3,4]
may be considered for the implementation.
Parallel computers have as a core structure a set
of interconnected processors. The optimal choice of interconnection for a
particular problem may not always be available. In fact, in practice the
interconnection usually takes place within some sort of plane two-dimensional
lattice. In the consideration of the parallel algorithm, it would be
interesting to explore the features of the two-dimensional graph arising from
the connections between destinations (edges), and to relate this to the lattice
of processor connectivity. It may be worthwhile to investigate certain
properties possessed by the processor graph, such as degree of symmetry and
homogeneity [5], as well as the extent to which it can be embedded in a
lattice.
An interesting consideration would be to recompute
routes, with certain nodes and edges removed. This may arise, for example, on
the California road network, when access to certain segments of the network has
been restricted due to a fire hazard or road traffic accident. The problem then
becomes one of utilizing the existing predetermined routes and modifying them,
rather than recalculating them all again using the initial dataset.
A relatively recent result on the dynamic
complexity of graph connectivity may prove to be useful in helping us achieve
this goal [6].
References:
[1] Batty
M. Parallel Route Planning for the London Underground, Diploma in Computer
Science, Computer Laboratory, 2007.
[2] https://www.cs.utah.edu/~lifeifei/SpatialDataset.htm
[3] Grama, Gupta, Karypis, Kumar. Introduction to Parallel Computing, Pearson Education, second
edition, 2005.
[4]
Akpan, O. Efficient parallel implementation of the Fox algorithm. Computer Science Department, Bowie State University, 2003.
[5] Modi
J. Parallel Algorithms and Matrix Computation, OUP, 1988.
[6] Samir Datta, Raghav Kulkarni, Anish Mukherjee,
Thomas Schwentick, and Thomas Zeume. 2018. Reachability Is in DynFO. J. ACM 65, 5, Article 33 (August 2018), 24 pages.