arXiv subjects

Antonio Fernández Anta

Publications and source records attributed to Antonio Fernández Anta.

48 records · Page 3Linked to original sources

arXiv2013

Online Parallel Scheduling of Non-uniform Tasks: Trading Failures for Energy

Consider a system in which tasks of different execution times arrive continuously and have to be executed by a set of processors that are prone to crashes and restarts. In this paper we model and study the impact of parallelism and failures on the competitiveness of such an online system. In a fault-free environment, a simple Longest-in-System scheduling policy, enhanced by a redundancy-avoidance mechanism, guarantees optimality in a long-term execution. In the presence of failures though, scheduling becomes a much more challenging task. In particular, no parallel deterministic algorithm can be competitive against an offline optimal solution, even with one single processor and tasks of only two different execution times. We find that when additional energy is provided to the system in the form of processor speedup, the situation changes. Specifically, we identify thresholds on the speedup under which such competitiveness cannot be achieved by any deterministic algorithm, and above which competitive algorithms exist. Finally, we propose algorithms that achieve small bounded competitive ratios when the speedup is over the threshold.

cs.DC↗

arXiv2013

Measuring the Impact of Adversarial Errors on Packet Scheduling Strategies

In this paper we explore the problem of achieving efficient packet transmission over unreliable links with worst case occurrence of errors. In such a setup, even an omniscient offline scheduling strategy cannot achieve stability of the packet queue, nor is it able to use up all the available bandwidth. Hence, an important first step is to identify an appropriate metric for measuring the efficiency of scheduling strategies in such a setting. To this end, we propose a relative throughput metric which corresponds to the long term competitive ratio of the algorithm with respect to the optimal. We then explore the impact of the error detection mechanism and feedback delay on our measure. We compare instantaneous error feedback with deferred error feedback, that requires a faulty packet to be fully received in order to detect the error. We propose algorithms for worst-case adversarial and stochastic packet arrival models, and formally analyze their performance. The relative throughput achieved by these algorithms is shown to be close to optimal by deriving lower bounds on the relative throughput of the algorithms and almost matching upper bounds for any algorithm in the considered settings. Our collection of results demonstrate the potential of using instantaneous feedback to improve the performance of communication systems in adverse environments.

cs.NI↗

arXiv2013

Reducing Search Lengths with Locally Precomputed Partial Random Walks

Random walks can be used to search a complex networks for a desired resource. To reduce the number of hops necessary to find the resource, we propose a search mechanism based on building random walks connecting together partial walks that have been precomputed at each network node in an initial stage. The resources found in each partial walk are registered in its associated Bloom filter. Searches can then jump over partial nodes in which the resource is not located, significantly reducing search length. However, additional unnecessary hops come from false positives at the Bloom filters. The analytic model provided predicts the expected search length of this mechanism, the optimal size of the partial walks and the corresponding optimal (shortest) expected search length. Simulation experiments are used to validate these predictions and to assess the impact of the number of partial walks precomputed in each node.

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arXiv2013

Improving Resource Location with Locally Precomputed Partial Random Walks

Random walks can be used to search complex networks for a desired resource. To reduce search lengths, we propose a mechanism based on building random walks connecting together partial walks (PW) previously computed at each network node. Resources found in each PW are registered. Searches can then jump over PWs where the resource is not located. However, we assume that perfect recording of resources may be costly, and hence, probabilistic structures like Bloom filters are used. Then, unnecessary hops may come from false positives at the Bloom filters. Two variations of this mechanism have been considered, depending on whether we first choose a PW in the current node and then check it for the resource, or we first check all PWs and then choose one. In addition, PWs can be either simple random walks or self-avoiding random walks. Analytical models are provided to predict expected search lengths and other magnitudes of the resulting four mechanisms. Simulation experiments validate these predictions and allow us to compare these techniques with simple random walk searches, finding very large reductions of expected search lengths.

cs.NI↗

arXiv2013

Routing for Energy Minimization with Discrete Cost Functions

Energy saving is becoming an important issue in the design and use of computer networks. In this work we propose a problem that considers the use of rate adaptation as the energy saving strategy in networks. The problem is modeled as an integral demand-routing problem in a network with discrete cost functions at the links. The discreteness of the cost function comes from the different states (bandwidths) at which links can operate and, in particular, from the energy consumed at each state. This in its turn leads to the non-convexity of the cost function, and thus adds complexity to solve this problem. We formulate this routing problem as an integer program, and we show that the general case of this problem is NP-hard, and even hard to approximate. For the special case when the step ratio of the cost function is bounded, we show that effective approximations can be obtained. Our main algorithm executes two processes in sequence: relaxation and rounding. The relaxation process eliminates the non-convexity of the cost function, so that the problem is transformed into a fractional convex program solvable in polynomial time. After that, a randomized rounding process is used to get a feasible solution for the original problem. This algorithm provides a constant approximation ratio for uniform demands and an approximation ratio of $O(\log^{β-1} d)$ for non-uniform demands, where $β$ is a constant and $d$ is the largest demand.

cs.NI↗

arXiv2012

Node Sampling using Random Centrifugal Walks

Sampling a network with a given probability distribution has been identified as a useful operation. In this paper we propose distributed algorithms for sampling networks, so that nodes are selected by a special node, called the \emph{source}, with a given probability distribution. All these algorithms are based on a new class of random walks, that we call Random Centrifugal Walks (RCW). A RCW is a random walk that starts at the source and always moves away from it. Firstly, an algorithm to sample any connected network using RCW is proposed. The algorithm assumes that each node has a weight, so that the sampling process must select a node with a probability proportional to its weight. This algorithm requires a preprocessing phase before the sampling of nodes. In particular, a minimum diameter spanning tree (MDST) is created in the network, and then nodes' weights are efficiently aggregated using the tree. The good news are that the preprocessing is done only once, regardless of the number of sources and the number of samples taken from the network. After that, every sample is done with a RCW whose length is bounded by the network diameter. Secondly, RCW algorithms that do not require preprocessing are proposed for grids and networks with regular concentric connectivity, for the case when the probability of selecting a node is a function of its distance to the source. The key features of the RCW algorithms (unlike previous Markovian approaches) are that (1) they do not need to warm-up (stabilize), (2) the sampling always finishes in a number of hops bounded by the network diameter, and (3) it selects a node with the exact probability distribution.

cs.DC↗

arXiv2012

Quid Pro Quo: A Mechanism for Fair Collaboration in Networked Systems

Collaboration may be understood as the execution of coordinated tasks (in the most general sense) by groups of users, who cooperate for achieving a common goal. Collaboration is a fundamental assumption and requirement for the correct operation of many communication systems. The main challenge when creating collaborative systems in a decentralized manner is dealing with the fact that users may behave in selfish ways, trying to obtain the benefits of the tasks but without participating in their execution. In this context, Game Theory has been instrumental to model collaborative systems and the task allocation problem, and to design mechanisms for optimal allocation of tasks. In this paper, we revise the classical assumptions and propose a new approach to this problem. First, we establish a system model based on heterogenous nodes (users, players), and propose a basic distributed mechanism so that, when a new task appears, it is assigned to the most suitable node. The classical technique for compensating a node that executes a task is the use of payments (which in most networks are hard or impossible to implement). Instead, we propose a distributed mechanism for the optimal allocation of tasks without payments. We prove this mechanism to be robust event in the presence of independent selfish or rationally limited players. Additionally, our model is based on very weak assumptions, which makes the proposed mechanisms susceptible to be implemented in networked systems (e.g., the Internet).

cs.GT↗

arXiv2012

Bisection (Band)Width of Product Networks with Application to Data Centers

The bisection width of interconnection networks has always been important in parallel computing, since it bounds the amount of information that can be moved from one side of a network to another, i.e., the bisection bandwidth. Finding its exact value has proven to be challenging for some network families. For instance, the problem of finding the exact bisection width of the multidimensional torus was posed by Leighton and has remained open for almost 20 years. In this paper we provide the exact value of the bisection width of the torus, as well as of several d-dimensional classical parallel topologies that can be obtained by the application of the Cartesian product of graphs. To do so, we first provide two general results that allow to obtain upper and lower bounds on the bisection width of a product graph as a function of some properties of its factor graphs. We also apply these results to obtain bounds for the bisection bandwidth of a d-dimensional BCube network, a recently proposed topology for data centers.

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arXiv2011

Failure Detectors in Homonymous Distributed Systems (with an Application to Consensus)

This paper addresses the consensus problem in homonymous distributed systems where processes are prone to crash failures and have no initial knowledge of the system membership ("homonymous" means that several processes may have the same identifier). New classes of failure detectors suited to these systems are first defined. Among them, the classes HΩ and HΣ are introduced that are the homonymous counterparts of the classes Ω and Σ, respectively. (Recall that the pair <Ω,Σ> defines the weakest failure detector to solve consensus.) Then, the paper shows how HΩ and HΣ can be implemented in homonymous systems without membership knowledge (under different synchrony requirements). Finally, two algorithms are presented that use these failure detectors to solve consensus in homonymous asynchronous systems where there is no initial knowledge of the membership. One algorithm solves consensus with , while the other uses only HΩ, but needs a majority of correct processes. Observe that the systems with unique identifiers and anonymous systems are extreme cases of homonymous systems from which follows that all these results also apply to these systems. Interestingly, the new failure detector class HΩ can be implemented with partial synchrony, while the analogous class AΩ defined for anonymous systems can not be implemented (even in synchronous systems). Hence, the paper provides us with the first proof showing that consensus can be solved in anonymous systems with only partial synchrony (and a majority of correct processes).

cs.DC↗

arXiv2011

Greening File Distribution: Centralized or Distributed?

Despite file-distribution applications are responsible for a major portion of the current Internet traffic, so far little effort has been dedicated to study file distribution from the point of view of energy efficiency. In this paper, we present a first approach at the problem of energy efficiency for file distribution. Specifically, we first demonstrate that the general problem of minimizing energy consumption in file distribution in heterogeneous settings is NP-hard. For homogeneous settings, we derive tight lower bounds on energy consumption, and we design a family of algorithms that achieve these bounds. Our results prove that collaborative p2p schemes achieve up to 50% energy savings with respect to the best available centralized file distribution scheme. Through simulation, we demonstrate that in more realistic cases (e.g., considering network congestion, and link variability across hosts) we validate this observation, since our collaborative algorithms always achieve significant energy savings with respect to the power consumption of centralized file distribution systems.

cs.NI↗

arXiv2011

Conauto-2.0: Fast Isomorphism Testing and Automorphism Group Computation

In this paper we present an algorithm, called conauto-2.0, that can efficiently compute a set of generators of the automorphism group of a graph, and test whether two graphs are isomorphic, finding an isomorphism if they are. This algorithm uses the basic individualization/refinement technique, and is an improved version of the algorithm conauto, which has been shown to be very fast for random graphs and several families of hard graphs. In this paper, it is proved that, under some circumstances, it is not only possible to prune the search space (using already found generators of the automorphism group), but also to infer new generators without the need of explicitly finding an automorphism of the graph. This result is especially suited for graphs with regularly connected components, and can be applied in any isomorphism testing and canonical labeling algorithm (that use the individualization/refinement technique) to significantly improve its performance. Additionally, a dynamic target cell selection function is used to adapt to different graphs. The resulting algorithm preserves all the nice features of conauto, but reduces the time for testing graphs with regularly connected components and other hard graph families. We run extensive experiments, which show that the most popular algorithms (namely, nauty, bliss, Traces, and saucy) are slower than conauto-2.0, among others, for the graph families based on components.

cs.DS↗

arXiv2011

Unbounded Contention Resolution in Multiple-Access Channels

A frequent problem in settings where a unique resource must be shared among users is how to resolve the contention that arises when all of them must use it, but the resource allows only for one user each time. The application of efficient solutions for this problem spans a myriad of settings such as radio communication networks or databases. For the case where the number of users is unknown, recent work has yielded fruitful results for local area networks and radio networks, although either a (possibly loose) upper bound on the number of users needs to be known, or the solution is suboptimal, or it is only implicit or embedded in other problems, with bounds proved only asymptotically. In this paper, under the assumption that collision detection or information on the number of contenders is not available, we present a novel protocol for contention resolution in radio networks, and we recreate a protocol previously used for other problems, tailoring the constants for our needs. In contrast with previous work, both protocols are proved to be optimal up to a small constant factor and with high probability for big enough number of contenders. Additionally, the protocols are evaluated and contrasted with the previous work by extensive simulations. The evaluation shows that the complexity bounds obtained by the analysis are rather tight, and that both protocols proposed have small and predictable complexity for many system sizes (unlike previous proposals).

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