Exploiting locality for data management in systems of limited bandwidth

Maggs, Bruce M.; Heide, Friedhelm Meyer auf der; Vöcking, Berthold; Westermann, Matthias

doi:10.1109/sfcs.1997.646117

Cited by 66 publications

(78 citation statements)

References 26 publications

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“…We obtain node and edge congestions which are within logarithmic factors of optimal, C node = O(C * node ·log n) and C edge = O(C * edge · log n), with high probability. Maggs et al [21] give a worst case edge congestion lower bound of Ω (C * edge · log n) for any oblivious routing algorithm in the 2-dimensional mesh. Therefore, in addition to constant stretch, the congestion we obtain is optimal, within constant factors, for oblivious algorithms.…”

Section: Geometric Networkmentioning

confidence: 99%

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Oblivious Routing for Sensor Network Topologies

Busch

Magdon‐Ismail

2010

Monographs in Theoretical Computer Science. An EATCS Series

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We present oblivious routing algorithms whose routing paths are constructed independent of each other, with no dependence on the routing history. Oblivious algorithms are inherently adaptive to dynamic packet traffic, exhibit low congestion, and require low maintenance. All these attributes make oblivious algorithms to be suitable for sensor networks which are characterized by their limited energy and computational resources. Specifically, low congestion provides load balancing, and low stretch provides low energy utilization. We present two simple oblivious routing algorithms. The first algorithm is for geometric networks in which nodes are embedded in the Euclidean plane. In this algorithm, a packet path is constructed by first choosing a random intermediate node in the space between the source and destination, and then the packet is sent to its destination through the intermediate node. In the second algorithm we study mesh networks, where the nodes are arranged in a 2-dimensional grid. Grids are interesting symmetric topologies which can be used as a testbed for designing efficient new routing algorithms in sensor networks. The oblivious algorithm in the mesh constructs the paths by decomposing the network into smaller submeshes in a hierarchical manner. This algorithm can be extended to d-dimensions, which makes it suitable for three-dimensional sensor network deployments, such as in buildings and tall structures. We analyze the algorithms in terms of the stretch and congestion of the resulting paths, and demonstrate that they exhibit near optimal performance.

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Section: Geometric Networkmentioning

confidence: 99%

“…We give an oblivious routing algorithm for the d-dimensional mesh with n nodes, that achieves congestion O(d · C * · log n), and stretch O(d 2 ), For the ddimensional mesh with n nodes, Maggs et al [21] give the lower bound…”

Section: Mesh Networkmentioning

confidence: 99%

Oblivious Routing for Sensor Network Topologies

Busch

Magdon‐Ismail

2010

Monographs in Theoretical Computer Science. An EATCS Series

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“…Maggs et al [20], give a strategy to select paths in the mesh such that the congestion achieved by the paths is C = O(dC * log n) with high probability. In that algorithm the dilation is D = O(m log n).…”

Section: Near Optimal Direct Routing On Meshmentioning

confidence: 99%

“…Busch et al [10] improve the dilation to be D = O(d 2 D * ), while preserving the congestion bound. The paths obtained by the algorithms in [10,20], are constructed from the concatenation of O(log n) dimension-by-dimension shortest paths between random nodes in the mesh. Since a dimension-by-dimension shortest path between two nodes on the mesh contains at most d bends, the number of bends that a packet makes is b = O(d log n).…”

Section: Near Optimal Direct Routing On Meshmentioning

confidence: 99%

Direct routing: Algorithms and complexity

et al. 2006

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Direct routing is the special case of bufferless routing where N packets, once injected into the network, must be delivered to their destinations without collisions. We give a general treatment of three facets of direct routing:(i) Algorithms. We present a polynomial time greedy direct algorithm which is worstcase optimal. We improve the bound of the greedy algorithm for special cases, by applying variants of the this algorithm to commonly used network topologies. In particular, we obtain near-optimal routing time for the tree, mesh, butterfly and hypercube.(ii) Complexity. By a reduction from Vertex Coloring, we show that optimal Direct Routing is inapproximable, unless P=NP.(iii) Lower Bounds for Buffering. We show that certain direct routing problems cannot be solved efficiently; in order to solve these problems, any routing algorithm needs buffers. We give non-trivial lower bounds on such buffering requirements for general routing algorithms. * A preliminary version of this

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“…Congestion minimization problems can be seen as equivalent to a robust optimization where one uses maximum edge congestion as a cost function; simply take the polytope consisting of all single-sink demands which are routable in G (this is a superset of our choice P). The construction in [13] uses meshes (grids), building on work of [4,14]. This construction does not seem to extend to the total cost model however, and we use instead a construction based on expanders, extending and simplifying a connection shown in earlier work [7].…”

Section: Introductionmentioning

confidence: 99%

Dynamic vs. Oblivious Routing in Network Design

2010

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Abstract. Consider the robust network design problem of finding a minimum cost network with enough capacity to route all traffic demand matrices in a given polytope. We investigate the impact of different routing models in this robust setting: in particular, we compare oblivious routing, where the routing between each terminal pair must be fixed in advance, to dynamic routing, where routings may depend arbitrarily on the current demand. Our main result is a construction that shows that the optimal cost of such a network based on oblivious routing (fractional or integral) may be a factor of Ω(log n) more than the cost required when using dynamic routing. This is true even in the important special case of the asymmetric hose model. This answers a question in [6], and is tight up to constant factors. Our proof technique builds on a connection between expander graphs and robust design for single-sink traffic patterns [7].

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Exploiting locality for data management in systems of limited bandwidth

Cited by 66 publications

References 26 publications

Oblivious Routing for Sensor Network Topologies

Oblivious Routing for Sensor Network Topologies

Direct routing: Algorithms and complexity

Dynamic vs. Oblivious Routing in Network Design

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