Efficient Bufferless Routing on Leveled Networks

Busch, Costas; Kelkar, Shailesh; Magdon‐Ismail, Malik

doi:10.1007/11549468_102

Cited by 2 publications

(2 citation statements)

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“…The bufferless efficiency ρ B (N, G) is the maximum possible value of the Q-bufferless efficiency over all batch problems, ρ B (N, G) = sup Q ρ B (Q; N, G). Our result shows that the bufferless efficiency is poly-logarithmicaly bounded, ρ B (N, G) = O(log 3 (n + N )), where n is the size of G. An interesting problem is to determine tighter asymptotic upper bounds as well as lower bounds for the bufferless efficiency for specific as well as arbitrary networks (for example, it is shown in [21] that the bufferless efficiency for leveled networks is only O(log(n + N ))).…”

Section: Main Resultmentioning

confidence: 95%

“…This enables us to control the positions of the packets and implicitly obtain the aforementioned paths P and a collision-free schedule on them. Hot-potato algorithms have been extensively studied for a variety of architectures such as the mesh and torus [7,9,10,14,16,18,19,20,25,26,29,30,31,39,48], hypercubes [13,15,26,28,42], trees [23,46], vertex-symmetric networks [36], and leveled networks [12,17,21]. Typically, by allowing packets to deviate slightly from their pre-selected paths, one obtains delivery times that are within poly-logarithmic factors of optimal.…”

Section: Batch Problemsmentioning

confidence: 99%

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Universal Bufferless Packet Switching

2007

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Abstract. A packet-switching algorithm specifies the actions of the nodes in order to deliver packets in the network. A packet-switching algorithm is universal if it applies to any network topology and for any batch communication problem on the network. A long standing open problem has concerned the existence of a universal packet-switching algorithm with near optimal performance guarantees for the class of bufferless networks where the buffer size for packets in transit is zero. We give a positive answer to this question. In particular, we give a universal bufferless algorithm which is within a poly-logarithmic factor from optimal for arbitrary batch problems:where T is the packet delivery time of our algorithm, T * is the optimal delivery time, n is the size of the network, and N is the number of packets. At the heart of our result is a new deterministic technique for constructing a universal bufferless algorithm by emulating a store-and-forward algorithm on a transformation of the network. The main idea is to replace packet buffering in the transformed network with packet circulation in regions of the original network. The cost of the emulation on the packet delivery time is proportional to the buffer sizes used by the store-and-forward algorithm. We obtain the advertised result by using a store-and-forward algorithm with logarithmic sized buffers. The resulting bufferless algorithm is constructive and it can be implemented in a distributed way.

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Section: Main Resultmentioning

confidence: 95%