Enyue Lu

Parallel routing algorithms for nonblocking electronic and photonic switching networks

We study the connection capacity of a class of rearrangeable nonblocking (RNB) and strictly nonblocking (SNB) networks with/without crosstalk-free constraint, model their routing problems as weak or strong edge-colorings of bipartite graphs, and propose efficient routing algorithms for these networks using parallel processing techniques. This class of networks includes networks constructed from banyan networks by horizontal concatenation of extra stages and/or vertical stacking of multiple planes. We present a parallel algorithm that runs in O(lg/sup 2/ N) time for the RNB networks of complexities ranging from O(N lg N) to O(N/sup 1.5/ lg N) crosspoints and parallel algorithms that run in O(min{d* lg N, /spl radic/N}) time for the SNB networks of O(N/sup 1.5/ lg N) crosspoints, using a completely connected multiprocessor system of N processing elements. Our algorithms can be translated into algorithms with an O(lg N lg lg N) slowdown factor for the class of N-processor hypercubic networks, whose structures are no more complex than a single plane in the RNB and SNB networks considered.

Finding two disjoint paths in a network with normalized α + -MIN-SUM objective function

Given a number α with 0 < α < 1, a network G = (V, E) and two nodes s and t in G, we consider the problem of finding two disjoint paths P1 and P2 from s to t such that length(P1) ≤ length(P2) and length(P1)+α·length(P2) is minimized. The paths may be node-disjoint or edge-disjoint, and the network may be directed or undirected. This problem has applications in reliable communication. We prove an approximation ratio

Hierarchical scheduling for DiffServ classes

{1+\alpha} \over {2\alpha}

High-speed crosstalk-free routing for optical multistage interconnection networks

for all four versions of this problem, and also show that this ratio cannot be improved for the two directed versions unless P = NP. We also present Integer Linear Programming formulations for all four versions of this problem. For a special case of this problem, we give a polynomial-time algorithm for finding optimal solutions.

Parallel routing and wavelength assignment for optical multistage interconnection networks

Due to its simplicity and scalability, the differentiated services (DiffServ) model is expected to be widely deployed across the Internet. For each DiffServ compliant router, the scheduling algorithm is critical in implementing per hop behaviors (PHBs), according to which packets are forwarded. We propose a hierarchical DiffServ scheduling (HDS) algorithm to support DiffServ classes on input-queued switches. The proposed HDS algorithm features in a hierarchical scheduling scheme that consists of two levels of schedulers. One level is the central scheduler which is designed to maximize the switch throughput by computing a maximal size matching between input ports and output ports. The other level is formed by input port schedulers which provide differentiated services by serving cells belonging to different classes dynamically. Using such a hierarchical scheme, the implementation complexity and the amount of information needed to be transmitted between input ports and the central scheduler are dramatically reduced compared with existing maximal weight matching based DiffServ scheduling algorithms. The tradeoff of its slightly worse delay performance is acceptable.

Scheduling with dynamic bandwidth allocation for DiffServ classes

Multistage interconnection networks (MINs) can be used to construct electro-optic switches. To implement crosstalk-free switching in such a switch, two I/O connecting paths cannot share a common switching element (SE). Thus, a permutation must be decomposed into partial permutations, each being routed through the switch without crosstalk. It was shown that any permutation can be decomposed into two semipermutations, and each is a maximum partial permutation realizable in one pass in an optical Benes network. However, the time complexity of existing decomposition algorithms for realizing connection requests is proportional to permutation size. In this paper, we reexamine the permutation capacity of MINs, present a simpler proof for semipermutation decomposability, and propose a parallel decomposition algorithm of logarithmic time. This algorithm is shown useful for optimally routing crosstalk-free paths in optical Benes networks in high-speed.

A Parallel Iterative Improvement Stable Matching Algorithm

Multistage interconnection networks (MINs) are among the most efficient switching architectures in terms of the number of switching elements (SEs) used. For optical MINs (OMINs), two I/O connections with neighboring wavelengths cannot share a common SE due to crosstalk. In this paper, we focus on the wavelength dilation approach, in which the I/O connections sharing a common SE will be assigned different wavelengths with enough wavelength spacing. We first study the permutation capacity of OMINs, then propose fast parallel routing and wavelength assignment algorithms for OMINs. By applying our permutation decomposition and graph coloring techniques, the proposed algorithms can route any permutation without crosstalk in wavelength-rearrangeable space-strict-sense Banyan networks and wavelength-rearrangeable space-rearrangeable Benes networks in polylogarithmic time using a linear number of processors.

A practical fast parallel routing architecture for Clos networks

The diverse service requirements of emerging Internet applications faster the need for flexible and scalable IP quality-of-service (QoS) schemes. Due to its simplicity and scalability, DiffServ is expected to be widely deployed across the Internet. Though DiffServ supporting scheduling algorithms for output-queueing (OQ) switches have been widely studied, there are few DiffServ scheduling algorithms for input-queueing (IQ) switches. In this paper, we propose the dynamic DiffServ scheduling (DDS) algorithm for IQ switches to provide dynamic bandwidth allocation for DiffServ classes. The basic idea of DDS is to schedule EF and AF traffic according to their minimum service rates with the reserved bandwidth and schedule AF and BE traffic fairly with the excess bandwidth. We evaluate the performance of DDS under bursty traffic arrivals and compare it with PQWRR, an existing scheduling algorithm suitable for supporting DiffServ for OQ switches. Simulations results show that DDS provides minimum bandwidth guarantees for EF and AF traffic and fair bandwidth allocation for BE traffic. DDS also achieves the delay and jitter performance for EF traffic close to that of PQWRR and the delay performance for AF traffic better than that of PQWRR at high loads. Using comparator-tree based arbitration components, it is feasible to implement DDS in hardware at high speed.

Fast reconfiguration algorithms for time, space, and wavelength dilated optical Benes networks

In this paper, we propose a new approach, parallel iterative improvement (PII), to solving the stable matching problem. This approach treats the stable matching problem as an optimization problem with all possible matchings forming its solution space. Since a stable matching always exists for any stable matching problem instance, finding a stable matching is equivalent to finding a matching with the minimum number (which is always zero) of unstable pairs. A particular PII algorithm is presented to show the effectiveness of this approach by constructing a new matching from an existing matching and using techniques such as randomization and greedy selection to speedup the convergence process. Simulation results show that the PII algorithm has better average performance compared with the classical stable matching algorithms and converges in n iterations with high probability. The proposed algorithm is also useful for some real-time applications with stringent time constraint.

A comparative study of efficient algorithms for partitioning a sequence into monotone subsequences

Clos networks are an important class of switching networks due to their modular structure and much lower cost compared with crossbars. For routing I/O permutations of Clos networks, sequential routing algorithms are too slow, and all known parallel algorithms are not practical. We present the algorithm-hardware codesign of a unified fast parallel routing architecture called distributed pipeline routing (DPR) architecture for rearrangeable nonblocking and strictly non-blocking Clos networks. The DPR architecture uses a linear interconnection structure and processing elements that performs only shift and logic AND operations. We show that a DPR architecture can route any permutation in rearrangeable nonblocking and strictly nonblocking Clos networks in OradicN time. The same architecture can be used to carry out control of any group of connection/disconnection requests for strictly nonblocking Clos networks in OradicN time. Several speeding-up techniques are also presented. This architecture is applicable to packet and circuit switches of practical sizes.