Constant Queue Route on a Mesh

Packet routing is an important problem in parallel computation since a single step of inter-processor communication can be thought of as a packet routing task. In this paper we present an optimal algorithm for packet routing on a mesh-connected computer. Two important criteria for judging a routing algorithm will be 1) its run time, i.e., the number of parallel steps it takes for the last packet to reach its destination, and 2) its queue size, i.e., the maximum number of packets that any node will have to store at any time during routing. We present a 2n - 2 step routing algorithm for an n x n mesh that requires a queue size of only 58. The previous best known result is a routing algorithm with the same time bound but with a queue size of 672. The time bound of 2n - 2 is optimal. A queue size of 672 is rather large for practical use. We believe that the queue size of our algorithm is practical. The improvement in the queue size is possible due to (from among other things) a new 3s + o(s) sorting algorithm for an s x s mesh

Efficient Algorithms for a Mesh-Connected Computer with Additional Global Bandwidth

This thesis shows that adding additional global bandwidths to a mesh-connected computer can greatly improve the performance. The goal of this project is to design algorithms for mesh-connected computers augmented with limited global bandwidth, so that we can further enhance our understanding of the parallel/serial nature of the problems on evolving parallel architectures. We do this by first solving several problems associated with fundamental data movement, then summarize ways to resolve different situations one may observe in data movement in parallel computing. This can help us to understand whether the problem is easily parallelizable on different parallel models. We give efficient algorithms to solve several fundamental problems, which include sorting, counting, fast Fourier transform, finding a minimum spanning tree, finding a convex hull, etc. We show that adding a small amount of global bandwidth makes a practical design that combines aspects of mesh and fully connected models to achieve the benefits of each. Most of the algorithms are optimal. For future work, we believe that algorithms with peak-power constrains can make our model well adapted to the recent architectures in high performance computing.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/150001/1/anyujie_1.pd

Deterministic 1-k routing on meshes with applications to worm-hole routing

In $1$-$k$ routing each of the $n^2$ processing units of an $n \times n$ mesh connected computer initially holds $1$ packet which must be routed such that any processor is the destination of at most $k$ packets. This problem reflects practical desire for routing better than the popular routing of permutations. $1$-$k$ routing also has implications for hot-potato worm-hole routing, which is of great importance for real world systems. We present a near-optimal deterministic algorithm running in \sqrt{k} \cdot n / 2 + \go{n} steps. We give a second algorithm with slightly worse routing time but working queue size three. Applying this algorithm considerably reduces the routing time of hot-potato worm-hole routing. Non-trivial extensions are given to the general $l$-$k$ routing problem and for routing on higher dimensional meshes. Finally we show that $k$-$k$ routing can be performed in \go{k \cdot n} steps with working queue size four. Hereby the hot-potato worm-hole routing problem can be solved in \go{k^{3/2} \cdot n} steps

An Elegant Algorithm for the Construction of Suffix Arrays

The suffix array is a data structure that finds numerous applications in string processing problems for both linguistic texts and biological data. It has been introduced as a memory efficient alternative for suffix trees. The suffix array consists of the sorted suffixes of a string. There are several linear time suffix array construction algorithms (SACAs) known in the literature. However, one of the fastest algorithms in practice has a worst case run time of $O(n^2)$. The problem of designing practically and theoretically efficient techniques remains open. In this paper we present an elegant algorithm for suffix array construction which takes linear time with high probability; the probability is on the space of all possible inputs. Our algorithm is one of the simplest of the known SACAs and it opens up a new dimension of suffix array construction that has not been explored until now. Our algorithm is easily parallelizable. We offer parallel implementations on various parallel models of computing. We prove a lemma on the $\ell$-mers of a random string which might find independent applications. We also present another algorithm that utilizes the above algorithm. This algorithm is called RadixSA and has a worst case run time of $O(n\log{n})$. RadixSA introduces an idea that may find independent applications as a speedup technique for other SACAs. An empirical comparison of RadixSA with other algorithms on various datasets reveals that our algorithm is one of the fastest algorithms to date. The C++ source code is freely available at http://www.engr.uconn.edu/~man09004/radixSA.zi