Book ChapterDOI
Optimal Interval Routing
Pierre Fraigniaud,Cyril Gavoille +1 more
- pp 785-796
TLDR
This paper investigates the study of optimal interval routing functions, that is routing functions that construct shortest paths, and derives practical tools that allow to determine if a network supports or not an optimal intervals routing function.Abstract:
Interval routing was introduced to reduce the size of the routing tables. This way of implementing routing functions is quite attractive but very few is known on the topological properties that should satisfy a network to admit an interval routing function satisfying particular constraints (shortest paths, limited number of intervals associated to each direction, etc). In this paper, we investigate the study of optimal interval routing functions, that is routing functions that construct shortest paths. In particular we derive practical tools that allow to determine if a network supports or not an optimal interval routing function. We describe large classes of networks that admit optimal interval routing functions. We also study the case of the usual networks that interconnect the processors of a distributed memory parallel computer.read more
Citations
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Proceedings ArticleDOI
Memory requirement for routing in distributed networks
Cyril Gavoille,Stéphane Pérennes +1 more
TL;DR: It is proved that for every shortest path routing scheme, for any constant e, O < c < 1, and for every integer d such that 3 ~ d < En, there exists a n-node network of maximum degree d that locally requires @(n log d) bits of memory on El(n) nodes.
Proceedings ArticleDOI
Memory requirement for universal routing schemes
Pierre Fraigniaud,Cyril Gavoille +1 more
TL;DR: This paper deals with the compact routing problem, that is implementing routing schemes that use a minimum memory size on each router, and improves this bound for stretch factors s < 2 by proving that any near-shortest path routing scheme uses a total of Q(n2) memory bits.
Journal ArticleDOI
The Complexity of Interval Routing on Random Graphs
TL;DR: It is shown that for suitably large n, there are suitable values of p such that for randomly chosen graphs G ∈?
Journal ArticleDOI
Worst Case Bounds for Shortest Path Interval Routing
Cyril Gavoille,Eric Guévremont +1 more
TL;DR: This paper constructs a networkG ofnnodes with Irs(G)??(n), thereby improving on the best known lower bound of
Journal ArticleDOI
The complexity of shortest path and dilation bounded interval routing
TL;DR: A routing algorithm with the dilation ⌈1.5D⌉ and the compactness O ( n log n ) on n -node networks with the diameter D .
References
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Book
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TL;DR: This chapter discusses sorting on a Linear Array with a Systolic and Semisystolic Model of Computation, which automates the very labor-intensive and therefore time-heavy and expensive process of manually sorting arrays.
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Parallel Processing with the Perfect Shuffle
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Journal ArticleDOI
The cube-connected cycles: a versatile network for parallel computation
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