Minimum Congestion Mapping in a Cloud

Bansal, Nikhil; Lee, Kang Won; Nagarajan, Viswanath; Zafer, Murtaza

doi:10.1137/110845239

Cited by 20 publications

(27 citation statements)

References 19 publications

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“…Eventually, each machine p i (1 ≤ i ≤ k) in practice, even assuming the links have a bandwidth of order of gigabytes of data per second, the amount of data that have been to be communicated can be in order of tera or peta bytes which generally dominates the overall computation cost [35]. 3 Partitioning based on the structure of the graph -with the goal of minimizing the amount of communication between the machines -is non-trivial; finding such a "good" partition itself might be prohibitively expensive and can be problem dependent. Some papers address this issue, see e.g., [40,3,39].…”

Section: Modelmentioning

confidence: 99%

Distributed Computation of Large-scale Graph Problems

Klauck¹,

Nanongkai²,

Pandurangan³

et al. 2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

158

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Motivated by the increasing need for fast distributed processing of large-scale graphs such as the Web graph and various social networks, we study a number of fundamental graph problems in the message-passing model, where we have k machines that jointly perform a computation on an arbitrary n-node (typically, n ≫ k) input graph. The graph is assumed to be randomly partitioned among the k ≥ 2 machines (a common implementation in many real world systems). The communication is point-to-point, and the goal is to minimize the time complexity, i.e., the number of communication rounds, of solving various fundamental graph problems.We present lower bounds that quantify the fundamental time limitations of distributively solving graph problems. We first show a lower bound of Ω(n/k) rounds for computing a spanning tree (ST) of the input graph. This result also implies the same bound for other fundamental problems such as computing a minimum spanning tree (MST), breadth-first tree (BFS), and shortest paths tree (SPT). We also show an Ω(n/k 2 ) * Division of Mathematical Sciences, Nanyang Technological University, Singapore 637371 & Centre for Quantum Technologies, Singapore 117543. E-mail: hklauck@gmail.com. This work is funded by the Singapore Ministry of Education (partly through the Academic Research Fund Tier 3 MOE2012-T3-1-009) and by the Singapore National Research Foundation.† KTH Royal Institute of Technology, Sweden, and University of Vienna, Austria E-mail: danupon@gmail.com. Work done while at ICERM, Brown University, USA, and Nanyang Technological University, Singapore. To complement our lower bounds, we also give algorithms for various fundamental graph problems, e.g., PageRank, MST, connectivity, ST verification, shortest paths, cuts, spanners, covering problems, densest subgraph, subgraph isomorphism, finding triangles, etc. We show that problems such as PageRank, MST, connectivity, and graph covering can be solved inÕ(n/k) time (the notationÕ hides polylog(n) factors and an additive polylog(n) term); this shows that one can achieve almost linear (in k) speedup, whereas for shortest paths, we present algorithms that run inÕ(n/ √ k) time (for (1 + ǫ)-factor approximation) and inÕ(n/k) time (for O(log n)-factor approximation) respectively.Our results are a step towards understanding the complexity of distributively solving large-scale graph problems.

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Section: Modelmentioning

confidence: 99%

Distributed Computation of Large-scale Graph Problems

Klauck¹,

Nanongkai²,

Pandurangan³

et al. 2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

158

View full text Add to dashboard Cite

show abstract

“…To the best of our knowledge, [6] and [2] (for online server migration), and [3], [15] (for online virtual network embeddings) are the only works to study network virtualization problems from an online algorithm perspective. The formal competitive migration problem is related to several classic optimization problems such as facility location, kserver problems, or online page migration.…”

Section: B Article Organizationmentioning

confidence: 99%

The Wide-Area Virtual Service Migration Problem: A Competitive Analysis Approach

Bieńkowski

Feldmann

Grassler

et al. 2014

IEEE/ACM Trans. Networking

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Abstract-Today's trend towards network virtualization and software-defined networking enables flexible new distributed systems where resources can be dynamically allocated and migrated to locations where they are most useful. This article proposes a competitive analysis approach to design and reason about online algorithms that find a good tradeoff between the benefits and costs of a migratable service. A competitive online algorithm provides worst-case performance guarantees under any demand dynamics, and without any information or statistical assumptions on the demand in the future. This is attractive especially in scenarios where the demand is hard to predict and can be subject to unexpected events.As a case study, we describe a service (e.g., an SAP server or a gaming application) that uses network virtualization to improve the Quality-of-Service (QoS) experienced by thin client applications running on mobile devices. By decoupling the service from the underlying resource infrastructure, it can be migrated closer to the current client locations while taking into account migration costs. We identify the major cost factors in such a system, and formalize the wide-area service migration problem. Our main contribution are a randomized and a deterministic online algorithm that achieve a competitive ratio of O(log n) in a simplified scenario, where n is the size of the substrate network. This is almost optimal. We complement our worst-case analysis with simulations in different specific scenarios, and also sketch a migration demonstrator.

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“…The embeddings of VNets is an intensively studied problem and there exists a large body of literature (e.g., [13,14,18,31]), and there also exist distributed computing approaches [16] and online algorithms [5,11]. Our work is orthogonal to this line of literature in the sense that we assume that an (arbitrary and not necessarily resource-optimal) embedding algorithm is given.…”

Section: Related Workmentioning

confidence: 99%

Adversarial topology discovery in network virtualization environments: a threat for ISPs?

2014

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Network virtualization is a new Internet paradigm which allows multiple virtual networks (VNets) to share the resources of a given physical infrastructure. The virtualization of entire networks is the natural next step after the virtualization of nodes and links.While the problem of how to embed a VNet ("guest network") on a given resource network ("host network") is algorithmically well-understood, much less is known about the security implications of this new technology. This paper introduces a new model to reason about one particular security threat: the leakage of information about the physical infrastructure-often a business secret.We initiate the study of this new problem and introduce the notion of request complexity which describes the number of VNet requests needed to fully disclose the substrate topology. We derive lower bounds and present algorithms achieving an asymptotically optimal request complexity for important graph classes such as trees, cactus graphs (complexity O(n)) as well as arbitrary graphs (complexity O(n 2 )). Moreover, a general motif-based topology discovery framework is described which exploits the poset structure of the VNet embedding relation.

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Minimum Congestion Mapping in a Cloud

Cited by 20 publications

References 19 publications

Distributed Computation of Large-scale Graph Problems

Distributed Computation of Large-scale Graph Problems

The Wide-Area Virtual Service Migration Problem: A Competitive Analysis Approach

Adversarial topology discovery in network virtualization environments: a threat for ISPs?

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