Marcin Bienkowski

A practical algorithm for constructing oblivious routing schemes

In a (randomized) oblivious routing scheme the path chosen for a request between a source s and a target t is independent from the current traffic in the network. Hence, such a scheme consists of probability distributions over s-t paths for every source-target pair s,t in the network.In a recent result [11] it was shown that for any undirected network there is an oblivious routing scheme that achieves a polylogarithmic competitive ratio with respect to congestion. Subsequently, Azar et al. [4] gave a polynomial time algorithm that for a given network constructs the best oblivious routing scheme, i.e. the scheme that guarantees the best possible competitive ratio. Unfortunately, the latter result is based on the Ellipsoid algorithm; hence it is unpractical for large networks.In this paper we present a combinatorial algorithm for constructing an oblivious routing scheme that guarantees a competitive ratio of O(log4n) for undirected networks. Furthermore, our approach yields a proof for the existence of an oblivious routing scheme with competitive ratio O(log3n), which is much simpler than the original proof from [11].

Dynamic load balancing in distributed hash tables

In Peer-to-Peer networks based on consistent hashing and ring topology, each server is responsible for an interval chosen (pseudo-) randomly on a unit circle. The topology of the network, the communication load, and the amount of data a server stores depend heavily on the length of its interval. Additionally, the nodes are allowed to join the network or to leave it at any time. Such operations can destroy the balance of the network, even if all the intervals had equal lengths in the beginning. This paper deals with the task of keeping such a system balanced, so that the lengths of intervals assigned to the nodes differ at most by a constant factor. We propose a simple fully distributed scheme, which works in a constant number of rounds and achieves optimal balance with high probability. Each round takes time at most

Competitive analysis for service migration in VNets

\mathcal{O}(\mathcal{D}+{\rm log n})

Online strategies for intra and inter provider service migration in virtual networks

, where

DYNAMIC SHARING OF A MULTIPLE ACCESS CHANNEL

\mathcal{D}

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

is the diameter of a specific network (e.g. Θ(log n) for Chord [15] and

Geometric aspects of online packet buffering: an optimal randomized algorithm for two buffers

\Theta(\frac{log n}{log log n})

Migrating and replicating data in networks

for the continous-discrete approach proposed by Naor and Wieder [12,11]). The scheme is a continuous process which does not have to be informed about the possible imbalance or the current size of the network to start working. The total number of migrations is within a constant factor from the number of migrations generated by the optimal centralized algorithm starting with the same initial network state.

An optimal lower bound for buffer management in multi-queue switches

Network virtualization promises a high flexibility by decoupling services from the underlying substrate network and allowing the virtual network to adapt to the needs of the service, e.g., by migrating servers or/and parts of the network. We study a system (e.g., a gaming application) where network virtualization is used to support thin client applications for mobile devices to improve their QoS. To deal with the dynamics of both the mobile clients as well as the ability to migrate services closer to the client location we advocate, in this paper, the use of competitive analysis. After identifying the parameters that characterize the cost-benefit tradeoff for this kind of application we propose an online migration strategy. The strength of the strategy is that it is robust with regards to any arbitrary request access pattern. In particular, it is close to the optimal offline algorithm that knows the access pattern in advance. In this paper we present both an optimal offline algorithm based on dynamic programming techniques to find the best migration paths for a given request sequence, and a O(¼ log n)-competitive migration strategy MIG where ¼ is the ratio between maximal and minimal link capacity in the substrate network for a simplified model. This is almost optimal for small ¼, as we also show that there are networks where no online algorithm can achieve a ratio below ©(log n/log log n). In contrast, the optimal solution without migration can only achieve a competitive ratio that is linear in the network diameter. Our simulations indicate that the competitive ratio of MIG is robust to the network size, and that the ratio is small if the request dynamics are limited and the requests are correlated.

Improved algorithms for dynamic page migration

Network virtualization allows one to build dynamic distributed systems in which resources can be dynamically allocated at locations where they are most useful. In order to fully exploit the benefits of this new technology, protocols need to be devised which react efficiently to changes in the demand. This paper argues that the field of online algorithms and competitive analysis provides useful tools to deal with and reason about the uncertainty in the request dynamics, and to design algorithms with provable performance guarantees. As a case study, we describe a system (e.g., a gaming application) where network virtualization is used to support thin client applications for mobile devices to improve their Quality-of-Service (QoS). By decoupling the service from the underlying resource infrastructure, it can be migrated closer to the current client locations while taking into account migration cost. This paper identifies the major cost factors in such a system, and formalizes the corresponding optimization problem. Both randomized and deterministic, gravity center based online algorithms are presented which achieve a good tradeoff between improved QoS and migration cost in the worst-case, both for service migration within an infrastructure provider as well as for networks supporting cross-provider migration. We report on our simulation results and also present an explicit construction of an optimal offline algorithm which can be used, e.g., to evaluate the competitive ratio empirically.