We study network optimization that considers power minimization as an objective. Studies have shown that mechanisms such as speed scaling can significantly reduce the power consumption of telecommunication networks by matching the consumption of each network element to the amount of processing required for its carried traffic. Most existing research on speed scaling focuses on a single network element in isolation. We aim for a network-wide optimization. Specifically, we study a routing problem with the objective of provisioning guaranteed speed/bandwidth for a given demand matrix while minimizing power consumption. Optimizing the routes critically relies on the characteristic of the speed-power curve , which is how power is consumed as a function of the processing speed . If is superadditive, we show that there is no bounded approximation in general for integral routing, i.e., each traffic demand follows a single path. This contrasts with the well-known logarithmic approximation for subadditive functions. However, for common speed-power curves such as polynomials , we are able to show a constant approximation via a simple scheme of randomized rounding. We also generalize this rounding approach to handle the case in which a nonzero startup cost appears in the speed-power curve, i.e., if if . We present an -approximation, and we discuss why coming up with an approximation ratio independent of the startup cost may be hard. Finally, we provide simulation results to validate our algorithmic approaches.

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 of these models 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 evenevent 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).

Abstract. In this paper we present a novel approach to the graph isomorphism problem. We combine a direct approach, that tries to find a mapping between the two input graphs using backtracking, with a (possibly partial) automorphism precomputing that allows to prune the search tree. We propose an algorithm, conauto, that has a space complexity of O(n 2 log n) bits. It runs in time O(n 5 ) with high probability if either one of the input graphs is a G(n, p) random graph, for p ∈ [ω(ln 4 n/n ln ln n), 1 − ω(ln 4 n/n ln ln n)]. We compare the practical performance of conauto with other popular algorithms, with an extensive collection of problem instances. Our algorithm behaves consistently for directed, undirected, positive, and negative cases. Additionally, when it is slower than any of the other algorithms, it is only by a small factor.

Random walks have been proven useful in several applications in networks. Some variants of the basic random walk have been devised pursuing a suitable trade-off between better performance and limited cost. A self-avoiding random walk (SAW) is one that tries not to revisit nodes, therefore covering the network faster than a random walk. Suggested as a network search mechanism, the performance of the SAW has been analyzed using essentially empirical studies.A strict analytical approach is hard since, unlike the random walk, the SAW is not a Markovian stochastic process. We propose an analytical model to estimate the average search length of a SAW when used to locate a resource in a network. The model considers single or multiple instances of the resource sought and the possible availability of one-hop replication in the network (nodes know about resources held by their neighbors). The model characterize networks by their size and degree distribution, without assuming a particular topology. It is, therefore, a mean-field model, whose applicability to real networks is validated by simulation. Experiments with sets of randomly built regular networks, Erdős-Rényi networks, and scale-free networks of several sizes and degree averages, with and without one-hop replication, show that model predictions *

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.