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

Design of Overlay Networks for Internet Multicast - Doctoral Dissertation, August 2002

Multicast is an efficient transmission scheme for supporting group communication in networks. Contrasted with unicast, where multiple point-to-point connections must be used to support communications among a group of users, multicast is more efficient because each data packet is replicated in the network – at the branching points leading to distinguished destinations, thus reducing the transmission load on the data sources and traffic load on the network links. To implement multicast, networks need to incorporate new routing and forwarding mechanisms in addition to the existing are not adequately supported in the current networks. The IP multicast are not adequately supported in the current networks. The IP multicast solution has serious scaling and deployment limitations, and cannot be easily extended to provide more enhanced data services. Furthermore, and perhaps most importantly, IP multicast has ignored the economic nature of the problem, lacking incentives for service providers to deploy the service in wide area networks. Overlay multicast holds promise for the realization of large scale Internet multicast services. An overlay network is a virtual topology constructed on top of the Internet infrastructure. The concept of overlay networks enables multicast to be deployed as a service network rather than a network primitive mechanism, allowing deployment over heterogeneous networks without the need of universal network support. This dissertation addresses the network design aspects of overlay networks to provide scalable multicast services in the Internet. The resources and the network cost in the context of overlay networks are different from that in conventional networks, presenting new challenges and new problems to solve. Our design goal are the maximization of network utility and improved service quality. As the overall network design problem is extremely complex, we divide the problem into three components: the efficient management of session traffic (multicast routing), the provisioning of overlay network resources (bandwidth dimensioning) and overlay topology optimization (service placement). The combined solution provides a comprehensive procedure for planning and managing an overlay multicast network. We also consider a complementary form of overlay multicast called application-level multicast (ALMI). ALMI allows end systems to directly create an overlay multicast session among themselves. This gives applications the flexibility to communicate without relying on service provides. The tradeoff is that users do not have direct control on the topology and data paths taken by the session flows and will typically get lower quality of service due to the best effort nature of the Internet environment. ALMI is therefore suitable for sessions of small size or sessions where all members are well connected to the network. Furthermore, the ALMI framework allows us to experiment with application specific components such as data reliability, in order to identify a useful set of communication semantic for enhanced data services

Analysis of algorithms for online routing and scheduling in networks

We study situations in which an algorithm must make decisions about how to best route and schedule data transfer requests in a communication network before each transfer leaves its source. For some situations, such as those requiring quality of service guarantees, this is essential. For other situations, doing work in advance can simplify decisions in transit and increase the speed of the network. In order to reflect realistic scenarios, we require that our algorithms be online, or make their decisions without knowing future requests. We measure the efficiency of an online algorithm by its competitive ratio, which is the maximum ratio, over all request sequences, of the cost of the online algorithm\u27s solution to that of an optimal solution constructed by knowing all the requests in advance.;We identify and study two distinct variations of this general problem. In the first, data transfer requests are permanent virtual circuit requests in a circuit-switched network and the goal is to minimize the network congestion caused by the route assignment. In the second variation, data transfer requests are packets in a packet-switched network and the goal is to minimize the makespan of the schedule, or the time that the last packet reaches its destination. We present new lower bounds on the competitive ratio of any online algorithm with respect to both network congestion and makespan.;We consider two greedy online algorithms for permanent virtual circuit routing on arbitrary networks with unit capacity links, and prove both lower and upper bounds on their competitive ratios. While these greedy algorithms are not optimal, they can be expected to perform well in many circumstances and require less time to make a decision, when compared to a previously discovered asymptotically optimal online algorithm. For the online packet routing and scheduling problem, we consider an algorithm which simply assigns to each packet a priority based upon its arrival time. No packet is delayed by another packet with a lower priority. We analyze the competitive ratio of this algorithm on linear array, tree, and ring networks

Optimal Permutation Routing for Low-dimensional Hypercubes

We consider the offline problem of routing a permutation of tokens on the nodes of a d-dimensional hypercube, under a queueless MIMD communication model (under the constraints that each hypercube edge may only communicate one token per communication step, and each node may only be occupied by a single token between communication steps). For a d-dimensional hypercube, it is easy to see that d communication steps are necessary. We develop a theory of “separability ” which enables an analytical proof that d steps suffice for the case d = 3, and facilitates an experimental verification that d steps suffice for d = 4. This result improves the upper bound for the number of communication steps required to route an arbitrary permutation on arbitrarily large hypercubes to 2d − 4. We also find an interesting side-result, that the number of possible communication steps in a d-dimensional hypercube is the same as the number of perfect matchings in a (d + 1)-dimensional hypercube, a combinatorial quantity for which there is no closed-form expression. Finally we present some experimental observations which may lead to a proof of a more general result for arbitrarily large dimension d. 2

How far can we go with OBS networks

Optical Burst Switching (OBS) was proposed ten years ago as an alternative switching paradigm in order to overcome some of the drawbacks of Optical Circuit Switching (OCS). While OBS is no more necessarily perceived as a competitor to OCS, but more of a more adapted switching for networks with bursty and highly dynamic traffic, there is still a debate around OBS, i.e., how far an OBS network can go in terms of throughput with no or limited burst losses. This thesis attempts to answer this question by investigating how to devise an upper bound on the throughput of an OBS network, assuming no recourse to electrical buffering is made at any intermediate node. We investigate both the burst scheduling and routing issues, with a larger focus on routing in three directions: (i) exploration of weighted k -shortest paths, (ii) revisiting load balancing, (iii) examining tree decomposition. Simulations have been conducted to compare and evaluate each of the new ideas with adapted (with respect to throughput upper bounding) previously proposed routing algorithms on different network and traffic instances. A comparison of the best upper bound with lower bounds obtained under various assumptions is presente