Greedy algorithm

About: Greedy algorithm is a research topic. Over the lifetime, 15347 publications have been published within this topic receiving 393945 citations.

Sparse Malicious False Data Injection Attacks and Defense Mechanisms in Smart Grids

Abstract: This paper discusses malicious false data injection attacks on the wide area measurement and monitoring system in smart grids. First, methods of constructing sparse stealth attacks are developed for two typical scenarios: 1) random attacks in which arbitrary measurements can be compromised; and 2) targeted attacks in which specified state variables are modified. It is already demonstrated that stealth attacks can always exist if the number of compromised measurements exceeds a certain value. In this paper, it is found that random undetectable attacks can be accomplished by modifying only a much smaller number of measurements than this value. It is well known that protecting the system from malicious attacks can be achieved by making a certain subset of measurements immune to attacks. An efficient greedy search algorithm is then proposed to quickly find this subset of measurements to be protected to defend against stealth attacks. It is shown that this greedy algorithm has almost the same performance as the brute-force method, but without the combinatorial complexity. Third, a robust attack detection method is discussed. The detection method is designed based on the robust principal component analysis problem by introducing element-wise constraints. This method is shown to be able to identify the real measurements, as well as attacks even when only partial observations are collected. The simulations are conducted based on IEEE test systems.

A polynomial-time algorithm for learning noisy linear threshold functions

Abstract: The authors consider the problem of learning a linear threshold function (a halfspace in n dimensions, also called a "perceptron"). Methods for solving this problem generally fall into two categories. In the absence of noise, this problem can be formulated as a linear program and solved in polynomial time with the ellipsoid algorithm (or interior point methods). On the other hand, simple greedy algorithms such as the perceptron algorithm seem to work well in practice and can be made noise tolerant; but, their running time depends on a separation parameter (which quantifies the amount of "wiggle room" available) and can be exponential in the description length of the input. They show how simple greedy methods can be used to find weak hypotheses (hypotheses that classify noticeably more than half of the examples) in polynomial time, without dependence on any separation parameter. This results in a polynomial-time algorithm for learning linear threshold functions in the PAC model in the presence of random classification noise. The algorithm is based on a new method for removing outliers in data. Specifically, for any set S of points in R/sup n/, each given to b bits of precision, they show that one can remove only a small fraction of S so that in the remaining set T, for every vector v, max/sub x/spl epsiv/T/(v/spl middot/x)/sup 2//spl les/poly(n,b)|T|/sup -1//spl Sigma//sub x/spl epsiv/T/(v/spl middot/x)/sup 2/. After removing these outliers, they are able to show that a modified version of the perceptron learning algorithm works in polynomial time, even in the presence of random classification noise.

Buffer Overflow Management in QoS Switches

Abstract: We consider two types of buffering policies that are used in network switches supporting Quality of Service (QoS). In the FIFO type, packets must be transmitted in the order in which they arrive; the constraint in this case is the limited buffer space. In the bounded-delay type, each packet has a maximum delay time by which it must be transmitted, or otherwise it is lost. We study the case of overloads resulting in packet loss. In our model, each packet has an intrinsic value, and the goal is to maximize the total value of transmitted packets. Our main contribution is a thorough investigation of some natural greedy algorithms in various models. For the FIFO model we prove tight bounds on the competitive ratio of the greedy algorithm that discards packets with the lowest value when an overflow occurs. We also prove that the greedy algorithm that drops the earliest packets among all low-value packets is the best greedy algorithm. This algorithm can be as much as 1.5 times better than the tail-drop greedy policy, which drops the latest lowest-value packets. In the bounded-delay model we show that the competitive ratio of any on-line algorithm for a uniform bounded-delay buffer is bounded away from 1, independent of the delay size. We analyze the greedy algorithm in the general case and in three special cases: delay bound 2, link bandwidth 1, and only two possible packet values. Finally, we consider the off-line scenario. We give efficient optimal algorithms and study the relation between the bounded-delay and FIFO models in this case.