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Scalable, Optimal Flow Routing in Datacenters via Local Link Balancing
"... Datacenter networks should support high network utilization. Yet today’s routing is typically load agnostic, so large flows can starve other flows if routed through overutilized links. Recent proposals for datacenter routing, such as centralized scheduling or endhost multipathing, do not offer opt ..."
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Datacenter networks should support high network utilization. Yet today’s routing is typically load agnostic, so large flows can starve other flows if routed through overutilized links. Recent proposals for datacenter routing, such as centralized scheduling or endhost multipathing, do not offer optimal throughput, and they suffer from scalability concerns and other limitations. We observe that most datacenter networks have a symmetry property that admits a better solution. We develop a simple, switchlocal algorithm called LocalFlow that routes the maximum multicommodity flow in these networks, while tolerating failures and asymmetry. LocalFlow evades existing hardness results by allowing flows to be fractionally split, but it minimizes the number of split flows by considering the aggregate flow per destination and allowing slack in the splitting. Through an optimization decomposition, we show that LocalFlow, in conjunction with unmodifed end hosts’ TCP, achieves an optimal solution. Splitting flows presents several new technical challenges that must be overcome in order to achieve high accuracy, interact properly with TCP, and be implementable on emerging standards for programmable, commodity switches. LocalFlow acts independently on each switch. This makes it highly scalable, allows it to adapt quickly to dynamic workloads, and enables flexibility in the deployment of its controlplane scheduling logic. We present detailed packetlevel simulations that demonstrate LocalFlow’s practicality and optimality, comparing it to a variety of alternative schemes and configurations, using distributions and traces from real datacenter workloads. 1.
Using optimization to break the epsilon barrier: A faster and simpler widthindependent algorithm for solving positive linear programs in parallel
 In Proceedings of the 26th ACMSIAM Symposium on Discrete Algorithms, SODA ’15
, 2015
"... We study the design of nearlylineartime algorithms for approximately solving positive linear programs (see [LN, STOC’93] [BBR, FOCS’97] [You, STOC’01] [KY, FOCS’07] [AK, STOC’08]). Both the parallel and the sequential deterministic versions of these algorithms require Õ(ε−4) iterations, a depende ..."
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Cited by 4 (2 self)
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We study the design of nearlylineartime algorithms for approximately solving positive linear programs (see [LN, STOC’93] [BBR, FOCS’97] [You, STOC’01] [KY, FOCS’07] [AK, STOC’08]). Both the parallel and the sequential deterministic versions of these algorithms require Õ(ε−4) iterations, a dependence that has not been improved since the introduction of these methods in 1993. Moreover, previous algorithms and their analyses rely on update steps and convergence arguments that are combinatorial in nature, but do not seem to arise naturally from an optimization viewpoint. In this paper, we leverage insights from optimization theory to construct a novel algorithm that breaks the longstanding Õ(ε−4) barrier. Our algorithm has a simple analysis and a clear motivation. Our work introduces a number of novel techniques, such as the combined application of gradient descent and mirror descent, and a truncated, smoothed version of the standard multiplicative update, which may be of independent interest. ar X iv
NearlyLinear Time Packing and Covering LP Solver with Faster Convergence Rate Than O(1/ε2)
, 2014
"... Packing and covering linear programs (LP) are an important class of problems that bridges computer science, operation research, and optimization. Efficient algorithms for solving such LPs have received significant attention in the past 20 years [LN93, PST95, BBR97, You01, ..."
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Cited by 1 (1 self)
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Packing and covering linear programs (LP) are an important class of problems that bridges computer science, operation research, and optimization. Efficient algorithms for solving such LPs have received significant attention in the past 20 years [LN93, PST95, BBR97, You01,
Decremental SingleSource Shortest Paths on Undirected Graphs in NearLinear Total Update Time
"... AbstractThe decremental singlesource shortest paths (SSSP) problem concerns maintaining the distances between a given source node s to every node in an nnode medge graph G undergoing edge deletions. While its static counterpart can be easily solved in nearlinear time, this decremental problem ..."
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AbstractThe decremental singlesource shortest paths (SSSP) problem concerns maintaining the distances between a given source node s to every node in an nnode medge graph G undergoing edge deletions. While its static counterpart can be easily solved in nearlinear time, this decremental problem is much more challenging even in the undirected unweighted case. In this case, the classic O(mn) total update time of Even and Shiloach (JACM 1981) In contrast to the previous results which rely on maintaining a sparse emulator, our algorithm relies on maintaining a socalled sparse (d, )hop set introduced by Cohen (JACM 2000) in the PRAM literature. A (d, )hop set of a graph G = (V, E) is a set E of weighted edges such that the distance between any pair of nodes in G can be (1 + )approximated by their dhop distance (given by a path containing at most d edges) on G = (V, E ∪E ). Our algorithm can maintain an (n o(1) , )hop set of nearlinear size in nearlinear time under edge deletions. It is the first of its kind to the best of our knowledge. To maintain the distances on this hop set, we develop a monotone boundedhop EvenShiloach tree. It results from extending and combining the monotone EvenShiloach tree of Henzinger, Krinninger, and Nanongkai (FOCS 2013) with the boundedhop SSSP technique of Bernstein (STOC 2013). These two new tools might be of independent interest.
Fast Partial Distance Estimation and Applications
"... We study approximate distributed solutions to the weighted allpairsshortestpaths (APSP) problem in the congest model. We obtain the following results. • A deterministic (1 + ε)approximation to APSP with running time O(ε−2n logn) rounds. The best previously known algorithm was randomized and slow ..."
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We study approximate distributed solutions to the weighted allpairsshortestpaths (APSP) problem in the congest model. We obtain the following results. • A deterministic (1 + ε)approximation to APSP with running time O(ε−2n logn) rounds. The best previously known algorithm was randomized and slower by a Θ(logn) factor. In many cases, routing schemes involve relabeling, i.e., assigning new names to nodes and that are used in distance and routing queries. It is known that relabeling is necessary to achieve running times of o(n / logn). In the relabeling model, we obtain the following results. • A randomized O(k)approximation to APSP, for any integer k> 1, running in Õ(n1/2+1/k +D) rounds, where D is the hop diameter of the network. This algorithm simplifies the best previously known result and reduces its approximation ratio from O(k log k) to O(k). Also, the new algorithm uses O(logn)bit labels, which is asymptotically optimal. • A randomized O(k)approximation to APSP, for any integer k> 1, running in time Õ((nD)1/2 · n1/k + D) and producing compact routing tables of size Õ(n1/k). The node labels consist of O(k logn) bits. This improves on the approximation ratio of Θ(k2) for tables of that size achieved by the best previously known algorithm, which terminates faster, in Õ(n1/2+1/k +D) rounds. In addition, we improve on the time complexity of the best known deterministic algorithm for distributed approximate Steiner forest.
Derandomization of Online Assignment Algorithms for Dynamic Graphs
, 2011
"... This paper analyzes different online algorithms for the problem of assigning weights to edges in a fullyconnected bipartite graph that minimizes the overall cost while satisfying constraints. Edges in this graph may disappear and reappear over time. Performance of these algorithms is measured using ..."
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This paper analyzes different online algorithms for the problem of assigning weights to edges in a fullyconnected bipartite graph that minimizes the overall cost while satisfying constraints. Edges in this graph may disappear and reappear over time. Performance of these algorithms is measured using simulations. This paper also attempts to derandomize the randomized online algorithm for this problem.