Recursive Estimation for Dynamical Systems with Different Delay Rates Sensor Network and Autocorrelated Process Noises

The recursive estimation problem is studied for a class of uncertain dynamical systems with different delay rates sensor network and autocorrelated process noises. The process noises are assumed to be autocorrelated across time and the autocorrelation property is described by the covariances between different time instants. The system model under consideration is subject to multiplicative noises or stochastic uncertainties. The sensor delay phenomenon occurs in a random way and each sensor in the sensor network has an individual delay rate which is characterized by a binary switching sequence obeying a conditional probability distribution. By using the orthogonal projection theorem and an innovation analysis approach, the desired recursive robust estimators including recursive robust filter, predictor, and smoother are obtained. Simulation results are provided to demonstrate the effectiveness of the proposed approaches

Small Candidate Set for Translational Pattern Search

In this paper, we study the following pattern search problem: Given a pair of point sets A and B in fixed dimensional space R^d, with |B| = n, |A| = m and n >= m, the pattern search problem is to find the translations T\u27s of A such that each of the identified translations induces a matching between T(A) and a subset B\u27 of B with cost no more than some given threshold, where the cost is defined as the minimum bipartite matching cost of T(A) and B\u27. We present a novel algorithm to produce a small set of candidate translations for the pattern search problem. For any B\u27 subseteq B with |B\u27| = |A|, there exists at least one translation T in the candidate set such that the minimum bipartite matching cost between T(A) and B\u27 is no larger than (1+epsilon) times the minimum bipartite matching cost between A and B\u27 under any translation (i.e., the optimal translational matching cost). We also show that there exists an alternative solution to this problem, which constructs a candidate set of size O(n log^2 n) in O(n log^2 n) time with high probability of success. As a by-product of our construction, we obtain a weak epsilon-net for hypercube ranges, which significantly improves the construction time and the size of the candidate set. Our technique can be applied to a number of applications, including the translational pattern matching problem

An Improved FPT Algorithm for the Flip Distance Problem

Given a set cal P of points in the Euclidean plane and two triangulations of cal P, the flip distance between these two triangulations is the minimum number of flips required to transform one triangulation into the other. The Parameterized Flip Distance problem is to decide if the flip distance between two given triangulations is equal to a given integer k. The previous best FPT algorithm runs in time O^*(kcdot c^k) (cleq 2times 14^11), where each step has fourteen possible choices, and the length of the action sequence is bounded by 11k. By applying the backtracking strategy and analyzing the underlying property of the flip sequence, each step of our algorithm has only five possible choices. Based on an auxiliary graph G, we prove that the length of the action sequence for our algorithm is bounded by 2|G|. As a result, we present an FPT algorithm running in time O^*(kcdot 32^k)

Randomized Parameterized Algorithms for the Kidney Exchange Problem

In order to increase the potential kidney transplants between patients and their incompatible donors, kidney exchange programs have been created in many countries. In the programs, designing algorithms for the kidney exchange problem plays a critical role. The graph theory model of the kidney exchange problem is to find a maximum weight packing of vertex-disjoint cycles and chains for a given weighted digraph. In general, the length of cycles is not more than a given constant L (typically 2 L 5), and the objective function corresponds to maximizing the number of possible kidney transplants. In this paper, we study the parameterized complexity and randomized algorithms for the kidney exchange problem without chains from theory. We construct two different parameterized models of the kidney exchange problem for two cases L = 3 and L 3, and propose two randomized parameterized algorithms based on the random partitioning technique and the randomized algebraic technique, respectively

Identification of ICS Security Risks toward the Analysis of Packet Interaction Characteristics Using State Sequence Matching Based on SF-FSM

This paper discusses two aspects of major risks related to the cyber security of an industrial control system (ICS), including the exploitation of the vulnerabilities of legitimate communication parties and the features abused by unauthorized parties. We propose a novel framework for exposing the above two types of risks. A state fusion finite state machine (SF-FSM) model is defined to describe multiple request-response packet pair sequence signatures of various applications using the same protocol. An inverted index of keywords in an industrial protocol is also proposed to accomplish fast state sequence matching. Then we put forward the concept of scenario reconstruction, using state sequence matching based on SF-FSM, to present the known vulnerabilities corresponding to applications of a specific type and version by identifying the packet interaction characteristics from the data flow in the supervisory control layer network. We also implement an anomaly detection approach to identifying illegal access using state sequence matching based on SF-FSM. An anomaly is asserted if none of the state sequence signatures in the SF-FSM is matched with a packet flow. Ultimately, an example based on industrial protocols is demonstrated by a prototype system to validate the methods of scenario reconstruction and anomaly detection

Improved Algorithms for Clustering with Outliers

Clustering is a fundamental problem in unsupervised learning. In many real-world applications, the to-be-clustered data often contains various types of noises and thus needs to be removed from the learning process. To address this issue, we consider in this paper two variants of such clustering problems, called k-median with m outliers and k-means with m outliers. Existing techniques for both problems either incur relatively large approximation ratios or can only efficiently deal with a small number of outliers. In this paper, we present improved solution to each of them for the case where k is a fixed number and m could be quite large. Particularly, we gave the first PTAS for the k-median problem with outliers in Euclidean space R^d for possibly high m and d. Our algorithm runs in O(nd((1/epsilon)(k+m))^(k/epsilon)^O(1)) time, which considerably improves the previous result (with running time O(nd(m+k)^O(m+k) + (1/epsilon)k log n)^O(1))) given by [Feldman and Schulman, SODA 2012]. For the k-means with outliers problem, we introduce a (6+epsilon)-approximation algorithm for general metric space with running time O(n(beta (1/epsilon)(k+m))^k) for some constant beta>1. Our algorithm first uses the k-means++ technique to sample O((1/epsilon)(k+m)) points from input and then select the k centers from them. Compared to the more involving existing techniques, our algorithms are much simpler, i.e., using only random sampling, and achieving better performance ratios