Mee Yee Chan

Schedulers for larger classes of pinwheel instances

The pinwheel is a hard-real-time scheduling problem for scheduling satellite ground stations to service a number of satellites without data loss. Given a multiset of positive integers (instance)A={a1,..., an}, the problem is to find an infinite sequence (schedule) of symbols from {1,2,...,n} such that there is at least one symboli within any interval of ai symbols (slots). Not all instancesA can be scheduled; for example, no “successful” schedule exists for instances whose density,ρ(A)=∑ii(l/ai), is larger than 1. It has been shown that all instances whose densities are less than a 0.5 density threshold can always be scheduled. If a schedule exists, another concern is the design of a fast on-line scheduler (FOLS) which can generate each symbol of the schedule in constant time. Based on the idea of “integer reduction,” two new FOLSs which can schedule different classes of pinwheel instances, are proposed in this paper. One uses “single-integer reduction” and the other uses “double-integer” reduction. They both improve the previous 0.5 result and have density thresholds of 13/20 and2/3, respectively. In particular, if the elements inA are large, the density thresholds will asymptotically approach In 2 and 1/R2, respectively.

On embedding rectangular grids in hypercubes

The following graph-embedding question is addressed: given a two-dimensional grid and the smallest hypercube with at least as many nodes as grid points, how can one assign grid points to hypercube nodes (with at most one grid point per node) so as to keep grid neighbors near each other in the cube? An embedding scheme for an infinite class of two-dimensional grids is given that keeps grid neighbors within a distance of two apart. >

Linear-Time haplotype inference on pedigrees without recombinations

In this paper, a linear-time algorithm, which is optimal, is presented to solve the haplotype inference problem for pedigree data when there are no recombinations and the pedigree has no mating loops. The approach is based on the use of graphs to capture SNP, Mendelian and parity constraints of the given pedigree.

Efficient constrained multiple sequence alignment with performance guarantee

The constrained multiple sequence alignment problem is to align a set of sequences subject to a given constrained sequence, which arises from some knowledge of the structure of the sequences. This paper presents new algorithms for this problem, which are more efficient in terms of time and space (memory) than the previous algorithms and with a worst-case guarantee on the quality of the alignment. Saving the space requirement by a quadratic factor is particularly significant as the previous O(n/sup 4/)-space algorithm has limited application due to its huge memory requirement. Experiments on real data sets confirm that our new algorithms show improvements in both alignment quality and resource requirements.

Dilation-5 embedding of 3-dimensional grids into hypercubes

We present an algorithm to map the nodes of a 3-dimensional grid to the nodes of its optimal hypercube on a one-to-one basis with dilation at most 5.<<ETX>>

A parallel algorithm for an efficient mapping of grids in hypercubes

The authors parallelize the embedding strategy for mapping any two-dimensional grid into its optimal hypercube with minimal dilation. The parallelization allows each hypercube node to independently determine, in constant time, which grid node it will simulate and the communication paths it will take to reach the hypercube nodes that simulate its grid-neighbors. The paths between grid-neighbors are chosen in such a way as to curb the congestion at each hypercube node and across each hypercube edge. Explicity, the node congestion for the embedding is at most 6, one above optimal, while the edge congestion is at most 5. >

Construction of the Nearest Neighbor Embracing Graph of a Point Set

This paper gives optimal algorithms for the construction of the Nearest Neighbor Embracing Graph (NNE-graph) of a given point set V of size n in the k-dimensional space (k-D) for k = 2,3. The NNE-graph provides another way of connecting points in a communication network, which has lower expected degree at each point and shorter total length of connections with respect to those using Delaunay triangulation. In fact, the NNE-graph can also be used as a tool to test whether a point set is randomly generated or has some particular properties.We show that in 2-D the NNE-graph can be constructed in optimal

Construction of the nearest neighbor embracing graph of a point set

\Theta(n^2)