A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓ p norms. We address this problem by introducing the concept of an All-norm ρ-approximation algorithm, which supplies one solution that guarantees ρ-approximation to all ℓ p norms simultaneously. Specifically, we consider the problem of scheduling in the restricted assignment model, where there are m machines and n jobs, each is associated with a subset of the machines and should be assigned to one of them. Previous work considered approximation algorithms for each norm separately. Lenstra et al.[11] showed a 2-approximation algorithm for the problem with respect to the ℓ ∞ norm. For any fixed ℓ p norm the previously known approximation algorithm has a performance of θ(p). We provide an all-norm 2-approximation polynomial algorithm for the restricted assignment problem. On the other hand, we show that for any given ℓ p norm (p > 1) there is no PTAS unless P=NP by showing an APXhardness result. We also show for any given ℓ p norm a FPTAS for any fixed number of machines.

Churn prediction aims to identify subscribers who are about to transfer their business to a competitor. Since the cost associated with customer acquisition is much greater than the cost of customer retention, churn prediction has emerged as a crucial Business Intelligence (BI) application for modern telecommunication operators. The dominant approach to churn prediction is to model individual customers and derive their likelihood of churn using a predictive model. Recent work has shown that analyzing customers' interactions by assessing the social vicinity of recent churners can improve the accuracy of churn prediction. We propose a novel framework, termed Group-First Churn Prediction, which eliminates the a priori requirement of knowing who recently churned. Specifically, our approach exploits the structure of customer interactions to predict which groups of subscribers are most prone to churn, before even a single member in the group has churned. Our method works by identifying closely-knit groups of subscribers using second order social metrics derived from information theoretic principles. The interactions within each group are then analyzed to identify social leaders. Based on Key Performance Indicators that are derived from these groups, a novel statistical model is used to predict the churn of the groups and their members. Our experimental results, which are based on data from a telecommunication operator with approximately 16 million subscribers, demonstrate the unique advantages of the proposed method. We further provide empirical evidence that our method captures social phenomena in a highly significant manner.

The concept of Quality of Service (QoS) networks has gained growing attention recently, as the traffic volume in the Internet constantly increases, and QoS guarantees are essential to ensure proper operation of most communication based applications. A QoS switch serves m incoming queues by transmitting packets arriving at these queues through one output port, one packet per time unit. Each packet is marked with a value indicating its guaranteed quality of service. Since the queues have bounded capacity and the rate of arriving packets can be much higher than the transmission rate, packets can be lost due to insufficient queue space. The goal is to maximize the total value of transmitted packets. This problem encapsulates two dependent questions: admission control, namely which packets to discard in case of queue overflow, and scheduling, i.e. which queue to use for transmission in each time unit. We use competitive analysis to study online switch performance in QoS based networks. Specifically, we provide a novel generic technique that decouples the admission control and scheduling problems. Our technique transforms any single queue admission control strategy (preemptive or nonpreemptive) to a scheduling and admission control algorithm for our general m queues model, whose competitive ratio is at most twice the competitive ratio of the given admission control strategy. We use our technique to derive concrete algorithms for the general preemptive and nonpreemptive cases, as well as for the interesting special cases of the 2-value model and the unit value model. To the best of our knowledge this is the first result combining both scheduling and admission control decisions for arbitrary packets sequences in multi-queue switches. We also provide a 1.58-competitive randomized algorithm for the unit value case. This case is interesting by itself since most current networks (e.g.

Recently, approximation analysis has been extensively used to study algorithms for routing weighted packets in various network settings. Although different techniques were applied in the analysis of diverse models, one common property was evident: The analysis of input sequences composed solely of two different values is always substantially easier, and many results are known only for restricted value sequences. Motivated by this, we introduce our zero-one principle for switching networks which characterizes a wide family of algorithms for which achieving capproximation (as well as c-competitiveness) with respect to sequences composed of 0's and 1's implies achieving c-approximation. The zero-one principle proves to be very efficient in the design of switching algorithms, and substantially facilitates their analysis. We present three applications. First, we consider the Multi-Queue Switching model and design a 3-competitive algorithm, improving the result from [12]. Second, we study the Dynamic Routing problem on a line topology of length k and present a k-competitive algorithm, which improves and generalizes the results from [2,21]. As a third application, we consider the work of [20], that compares the performance of local algorithms to the global optimum in various network topologies, and generalize their results from 2-value sequences to arbitrary value sequences.

We investigate the problem of routing traffic through a congested network in an environment of non-cooperative users. We use the worst-case coordination ratio suggested by Koutsoupias and Papadimitriou to measure the performance degradation due to the lack of a centralized traffic regulating authority. We provide a full characterization of the worst-case coordination ratio in the restricted assignment and unrelated parallel links model. In particular, we quantify the tradeoff between the "negligibility" of the traffic controlled by each user and the worst-case coordination ratio. We analyze both pure and mixed strategies systems and identify the range where their performance is similar.

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A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓ p norms. We address this problem by introducing the concept of an All-norm ρ-approximation algorithm, which supplies one solution that guarantees ρ-approximation to all ℓ p norms simultaneously. Specifically, we consider the problem of scheduling in the restricted assignment model, where there are m machines and n jobs, each is associated with a subset of the machines and should be assigned to one of them. Previous work considered approximation algorithms for each norm separately. Lenstra et al.[11] showed a 2-approximation algorithm for the problem with respect to the ℓ ∞ norm. For any fixed ℓ p norm the previously known approximation algorithm has a performance of θ(p). We provide an all-norm 2-approximation polynomial algorithm for the restricted assignment problem. On the other hand, we show that for any given ℓ p norm (p > 1) there is no PTAS unless P=NP by showing an APXhardness result. We also show for any given ℓ p norm a FPTAS for any fixed number of machines.

We investigate the problem of routing traffic through a congested network in an environment of non-cooperative users. We use the worst-case coordination ratio suggested by Koutsoupias and Papadimitriou to measure the performance degradation due to the lack of a centralized traffic regulating authority. We provide a full characterization of the worst-case coordination ratio in the restricted assignment and unrelated parallel links model. In particular, we quantify the tradeoff between the "negligibility" of the traffic controlled by each user and the worst-case coordination ratio. We analyze both pure and mixed strategies systems and identify the range where their performance is similar.