Work-preserving emulations of fixed-connection networks

Koch, Richard; Leighton, Tom; Maggs, Bruce M.; Rao, S. Srinivasa

doi:10.1145/73007.73029

Cited by 49 publications

(7 citation statements)

References 25 publications

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“…In particular this means that any computation performed by G k , could be performed by G x in constant slowdown (see Maggs and Schwabe [1998] and Koch et al [1997] for an overview on the literature of real-time emulations).…”

Section: Emulating General Graphs-smoothness Is Everythingmentioning

confidence: 99%

Novel architectures for P2P applications

Naor

Wieder

2007

ACM Trans. Algorithms

116

154

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We propose a new approach for constructing P2P networks based on a dynamic decomposition of a continuous space into cells corresponding to servers. We demonstrate the power of this approach by suggesting two new P2P architectures and various algorithms for them. The first serves as a DHT (distributed hash table) and the other is a dynamic expander network. The DHT network, which we call Distance Halving, allows logarithmic routing and load while preserving constant degrees. It offers an optimal tradeoff between degree and path length in the sense that degree d guarantees a path length of O(log d n). Another advantage over previous constructions is its relative simplicity. A major new contribution of this construction is a dynamic caching technique that maintains low load and storage, even under the occurrence of hot spots. Our second construction builds a network that is guaranteed to be an expander. The resulting topologies are simple to maintain and implement. Their simplicity makes it easy to modify and add protocols. A small variation yields a DHT which is robust against random Byzantine faults. Finally we show that, using our approach, it is possible to construct any family of constant degree graphs in a dynamic environment, though with worse parameters. Therefore, we expect that more distributed data structures could be designed and implemented in a dynamic environment.

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Section: Emulating General Graphs-smoothness Is Everythingmentioning

confidence: 99%

Novel architectures for P2P applications

Naor

Wieder

2007

ACM Trans. Algorithms

116

154

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“…Koch et al in [7], and Maggs and Schwabe in [11] address the problem of performing network emulations via embeddings.…”

Section: Related Workmentioning

confidence: 99%

Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules

1999

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In 1988, Leighton, Maggs, and Rao showed that for any network and any set of packets whose paths through the network are fixed and edge-simple, there exists a schedule for routing the packets to their destinations in O(c+d) steps using constant-size queues, where c is the congestion of the paths in the network, and d is the length of the longest path. The proof, however, used the Lovász Local Lemma and was not constructive. In this paper, we show how to find such a schedule in O(m(c+d)(log P) 4 (log log P)) time, with probability 1−1/P β , for any positive constant β, where P is the sum of the lengths of the paths taken by the packets in the network, and m is the number of edges used by some packet in the network. We also show how to parallelize the algorithm so that it runs in NC. The method that we use to construct the schedules is based on the algorithmic form of the Lovász Local Lemma discovered by Beck.

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“…These shorter linear arrays simulate their subarrays independently for some number of steps, and then must communicate with their neighbors to update the information near their boundaries. (For more details on this type of simulation, see [7] and [13].) If we divide each linear array into overlapping arrays of length (1 + ε) log M, we can store the short overlapping arrays in the lower linear arrays as we stored the disjoint blocks of length log M in the stack allocation algorithm, and use them to simulate the full linear array.…”

Section: Extensions Of the Basic Network And Algorithmmentioning

confidence: 99%

Efficient Algorithms for Dynamic Allocation of Distributed Memory

Leighton

Schwabe

1999

Algorithmica

Self Cite

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We consider the problem of dynamically allocating and deallocating local memory resources among multiple users in a parallel or distributed system. Given a group of independent users and a collection of interconnected local memory devices, we want to render the fragmentation of the memory resources irrelevant by allowing any user to allocate space for his or her purposes as long as there is space available anywhere in the system. In effect, we would like it to appear to the users as though they are allocating memory from a single central pool of memory, even though the space is distributed throughout the system.Our goal is to devise an on-line allocation algorithm that minimizes two cost measures: first, the fraction of unused space, which arises due to fragmentation of the memory; second, the slowdown needed by the system to service user requests, which arises due to the contention for access to the memory devices. We solve this distributed dynamic allocation problem in near-optimal fashion by devising an algorithm that allows the memory to be used to 100% of capacity despite the fragmentation and guarantees that service delays will always be within a constant factor of optimal. The algorithm is completely on-line (no foreknowledge of user activity is assumed) and can accommodate any sequence of allocations and deallocations by the users that does not violate global memory bounds.We also consider the distributed dynamic allocation problem in the more restrictive setting where the local memory devices are connected by a low-degree fixed-connection network, rather than being fully interconnected. In this case, communication costs must be more explicitly considered in our allocation algorithms. We give allocation algorithms for butterfly and hypercube networks, and prove necessary and sufficient conditions on the total amount of memory space needed for near-optimal algorithms to exist.

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Work-preserving emulations of fixed-connection networks

Cited by 49 publications

References 25 publications

Novel architectures for P2P applications

Novel architectures for P2P applications

Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules

Efficient Algorithms for Dynamic Allocation of Distributed Memory

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