Reinhardt Euler

On the completability of incomplete Latin squares

We introduce the notion of an availability matrix and apply a theorem of Frobenius-Konig to obtain necessary and sufficient conditions for the completability of an incomplete Latin row. We consider the related problem for two such rows within the framework of (1,2)-permutations and give solutions for several special cases. We also show how to extend these results to more than two rows. Finally, we present an integer programming formulation together with polyhedral results, and we discuss some consequences for class-teacher time-table problems.

A Distributed Multi-path Routing Algorithm to Balance Energy Consumption in Wireless Sensor Networks

Abstract A large use of applications of Wireless Sensor Networks (WSNs) pushes researchers to design and improve protocols and algorithms against the encountered challenges. One of the main goals is data gathering and routing to the base station (through the sink nodes) with lack of acknowledgement and where each node has no information about the network. Unbalanced energy consumption during the data routing process is an inherent problem in WSNs due to the limited energy capacity of the sensor nodes. In fact, WSNs require load balancing algorithms that make judicious use of the limited energy resource to route the gathered data to the sink node. In this paper, we propose a balanced multi-path routing algorithm by focusing on the residual energy and the hop count of each node to discover the best routes and to insert them into the routing table. The main idea of this algorithm comes from Ant Colony Optimization (ACO) and automata network modelization. Hence, the potential performance of the proposed algorithm relies on the best route to be selected which should have the minimum number of hops, the maximum energy and weighted energy between participating nodes to extend the lifetime of the network.

D-LPCN: A Distributed Least Polar-angle Connected Node Algorithm for Finding the Boundary of a Wireless Sensor Network

A boundary of wireless sensor networks (WSNs) can be used in many fields, for example, to monitor a frontier or a secure place of strategic sensitive sites like oil fields or frontiers of a country. This situation is modeled as the problem of finding a polygon hull in a connected Euclidean graph, which represents a minimal set of connected boundary nodes. In this paper we propose a new algorithm called D-LPCN (Distributed Least Polar-angle Connected Node) which represents the distributed version of the LPCN algorithm introduced in [1]. In each iteration, any boundary node, except the first one, chooses its nearest polar angle node among its neighbors with respect to the node found in the previous iteration. The first starting node can be automatically determined using the Minimum Finding algorithm, which has two main advantages. The first one is that the algorithm works with any type of a connected network, given as planar or not. Furthermore, it takes into account any blocking situation and contains the necessary elements to avoid them. The second advantage is that the algorithm can determine all the boundaries of the different connected parts of the network. The proposed algorithm is validated using the CupCarbon, Tossim and Contiki simulators. It has also been implemented using real sensor nodes based on the TelosB and Arduino/XBee platforms. We have estimated the energy consumption of each node and we have found that the consumption of the network depends on the number of the boundary nodes and their neighbors. The simulation results show that the proposed algorithm is less energy consuming than the existing algorithms and its distributed version is less energy consuming than the centralized version.

Dimensionality reduction in data mining

Sampling-based dimensionality reduction technique.Eliminating linearly redundant combined dimensions.Providing a convenient way to generate correlated multivariate random variables.Maintaining the integrity of the original information.Reducing the dimension of data space without losing important information. The recent trends in collecting huge and diverse datasets have created a great challenge in data analysis. One of the characteristics of these gigantic datasets is that they often have significant amounts of redundancies. The use of very large multi-dimensional data will result in more noise, redundant data, and the possibility of unconnected data entities. To efficiently manipulate data represented in a high-dimensional space and to address the impact of redundant dimensions on the final results, we propose a new technique for the dimensionality reduction using Copulas and the LU-decomposition (Forward Substitution) method. The proposed method is compared favorably with existing approaches on real-world datasets: Diabetes, Waveform, two versions of Human Activity Recognition based on Smartphone, and Thyroid Datasets taken from machine learning repository in terms of dimensionality reduction and efficiency of the method, which are performed on statistical and classification measures.

FPGA implementation of Bayesian network inference for an embedded diagnosis

Critical systems, like Unmanned Aerial Systems (UAS) operate in uncertain environments and have to face unexpected obstacles, weather changes and sensor, hardware or software failures. Therefore, a health management system is needed to detect and locate the failure in real time. In this paper, we propose a Field Programmable Gate Array (FPGA) implementation based on a Bayesian network (BN) representation, that allows to continuously monitor the embedded system under time and resource constraints. The hardware implementation is generated by a specific off-line framework integrating a high-level synthesis tool. The proposal is evaluated on a hybrid reconfigurable device to show potential speed-up. Some variations on the hardware implementation are also explored to give the best trade-off between accuracy, performance and resource allocation.

Data Mining Techniques Applied to Wireless Sensor Networks for Early Forest Fire Detection

Nowadays, forest fires are a serious threat to the environment and human life. The monitoring system for forest fires should be able to make a real-time monitoring of the target region and the early detection of fire threats. In this paper, we present a new approach for forest fire detection based on the integration of Data Mining techniques into sensor nodes. The idea is to use a clustered WSN where each sensor node will individually decide on detecting fire using a classifier of Data Mining techniques. When a fire is detected, the corresponding node will send an alert through its cluster-head which will pass through gateways and other cluster-heads until it will reach the sink in order to inform the firefighters. We use the CupCarbon simulator to validate and evaluate our proposed approach. Through extensive simulation experiments, we show that our approach can provide a fast reaction to forest fires while consuming energy efficiently. 1

Bayesian network-based framework for the design of reconfigurable health management monitors

Modern small-size UAVs depend on highly complex architectures with many sensors and computer-controlled actuators. The size, weight and budget constraints leave little or no room for redundant systems. So all components must be reliable and any fault must be detected as early as possible. In this paper, we propose an adaptive, real-time, on-board system to continuously monitor sensors, software, and hardware components for the detection and diagnosis of failures by means of Bayesian networks. In particular, we propose an optimized hardware implementation of Bayesian Networks (BNs) for monitoring and exploiting the evidence. We consider FPGA for both performances and the ability to dynamically configure the hardware according to mission applications. Finally, we introduce an off-line framework that can generate FPGA implementations of the monitors for embedded systems under time and resource constraints.

A New Method for Estimation of Missing Data Based on Sampling Methods for Data Mining

Today we collect large amounts of data and we receive more than we can handle, the accumulated data are often raw and far from being of good quality they contain Missing Values and noise.

Coloring planar Toeplitz graphs and the stable set polytope

Cliques and odd cycles are well known to induce facet-de.ninginequalities for the stable set polytope. In graph coloring cliques are a class of n-critical graphs whereas odd cycles represent the class of 3-critical graphs. In the .rst part of this paper we generalize both notions to ( Kn \ e)-cycles, a new class of n-critical graphs, and discuss some implications for the class of in.nite planar Toeplitz graphs. More precisely, we show that any in.nite Toeplitz graph decomposes into a .nite number of connected and isomorphic components. Similar to the bipartite case, in.nite planar Toeplitz graphs can be characterized by a simple condition on their de.ning 0 –1 sequence. We then address the problem of coloring such graphs. Whereas they can always be 4-colored by a greedy-like algorithm, we are able to fully characterize the subclass of 3-chromatic such graphs. As a corollary, we obtain a K5 onig-type characterization of this class by means of (K4 \ e)-cycles. In the second part, we turn to polyhedral theory and show that (Kn \ e)-cycles give rise to a new class of facet-de.ning inequalities for the stable set polytope. Then we show how Haj8 os’ construction can be used to further generalize (Kn \ e)-cycles thereby providinga very large class of n-critical graphs which are still facet-inducing for the associated stable set polytope.

Boundary node failure detection in wireless sensor networks

Wireless Sensor Networks (WSNs) are an important tool for monitoring strategic and dangerous sites where high security is required. Failure detection for sensor nodes in this specified application is a major concern. The failure of any system may cause losses such as economical, equipment damage and even risks for human lives. Moreover, failures are unavoidable in WSNs due to hardware constraints, hostile environment, unattended deployment and limited resources. This paper proposes a fully distributed approach, called Boundary Node Failure Detection (BNFD), for an efficient boundary control based on the determination of the WSN boundary. This one is determined using an algorithm which has the property to determine in each iteration the one-hop neighbor of the current boundary sensor. Hence, each boundary sensor knows its direct next boundary neighbor and can communicate with it in order to periodically test its presence. When a situation of failure is detected, a network restructuring will be launched to find a new boundary and an alarm will be triggered. The proposed approach has been implemented and simulated with the Castalia simulator. The simulation results show that the proposed method is energy efficient.