Proceedings of the 84th European Study Group Mathematics with Industry (SWI 2012), Eindhoven, January 30 - February 3, 2012

Introduction There are a few welldefined moments when mathematicians can get in contact with relevant unsolved problems proposed by the industry. One such a moment is the socalled "Study Group". The concept of the Study Group is rather simple and quite efficient: A group of mathematicians (of very different expertise) work together for one week. As a rule, on a Monday the industrial problems are presented by their owners, then few research groups selforganize around the proposed problems and work intensively until Friday, when the main findings are presented. The insight obtained via mathematical modeling together with the transfer of suitable mathematical technology usually lead the groups to adequate approximate solutions. As a direct consequence of this fact, the problem owners often decide to benefit more from such knowledge transfer and suggest related followup projects. In the period January 31– February 3, 2012, it was the turn of the Department of Mathematics and Computer Science of the Eindhoven University of Technology to organize and to host the "Studiegroep Wiskunde met de Industrie/Study Group Mathematics with the Industry" (shortly: SWI 2012, but also referred to as ESG 84, or as the 84th European Study Group with Industry). This was the occasion when about 80 mathematicians enjoyed working on six problems. Most of the participants were coming from a Dutch university, while a few were from abroad (e.g. from UK, Germany, France, India, Russia, Georgia, Turkey, India, and Sri Lanka). The open industrial problems were proposed by Endinet, Philips Lighting, Thales, Marin, Tata Steel, and Bartels Engineering. Their solutions are shown in this proceedings. They combine ingenious mathematical modeling with specific mathematical tools like geometric algorithms, combinatorial optimization of networks, identification of parameters and model structures, probability theory, and statistical data analysis. It is worth mentioning that this scientific proceedings is accompanied by a popular proceedings, written by Ionica Smeets, containing layman’s descriptions of the proposed problems and of the corresponding results

Proceedings of the 84th European Study Group Mathematics with Industry (SWI 2012), Eindhoven, January 30 - February 3, 2012

Introduction There are a few welldefined moments when mathematicians can get in contact with relevant unsolved problems proposed by the industry. One such a moment is the socalled "Study Group". The concept of the Study Group is rather simple and quite efficient: A group of mathematicians (of very different expertise) work together for one week. As a rule, on a Monday the industrial problems are presented by their owners, then few research groups selforganize around the proposed problems and work intensively until Friday, when the main findings are presented. The insight obtained via mathematical modeling together with the transfer of suitable mathematical technology usually lead the groups to adequate approximate solutions. As a direct consequence of this fact, the problem owners often decide to benefit more from such knowledge transfer and suggest related followup projects. In the period January 31– February 3, 2012, it was the turn of the Department of Mathematics and Computer Science of the Eindhoven University of Technology to organize and to host the "Studiegroep Wiskunde met de Industrie/Study Group Mathematics with the Industry" (shortly: SWI 2012, but also referred to as ESG 84, or as the 84th European Study Group with Industry). This was the occasion when about 80 mathematicians enjoyed working on six problems. Most of the participants were coming from a Dutch university, while a few were from abroad (e.g. from UK, Germany, France, India, Russia, Georgia, Turkey, India, and Sri Lanka). The open industrial problems were proposed by Endinet, Philips Lighting, Thales, Marin, Tata Steel, and Bartels Engineering. Their solutions are shown in this proceedings. They combine ingenious mathematical modeling with specific mathematical tools like geometric algorithms, combinatorial optimization of networks, identification of parameters and model structures, probability theory, and statistical data analysis. It is worth mentioning that this scientific proceedings is accompanied by a popular proceedings, written by Ionica Smeets, containing layman’s descriptions of the proposed problems and of the corresponding results

Fast Parallel Algorithms on a Class of Graph Structures With Applications in Relational Databases and Computer Networks.

The quest for efficient parallel algorithms for graph related problems necessitates not only fast computational schemes but also requires insights into their inherent structures that lend themselves to elegant problem solving methods. Towards this objective efficient parallel algorithms on a class of hypergraphs called acyclic hypergraphs and directed hypergraphs are developed in this thesis. Acyclic hypergraphs are precisely chordal graphs and their subclasses, and they have applications in relational databases and computer networks. In this thesis, first, we present efficient parallel algorithms for the following problems on graphs. (1) determining whether a graph is strongly chordal, ptolemaic, or a block graph. If the graph is strongly chordal, determine the strongly perfect vertex elimination ordering. (2) determining the minimal set of edges needed to make an arbitrary graph strongly chordal, ptolemaic, or a block graph. (3) determining the minimum cardinality dominating set, connected dominating set, total dominating set, and the domatic number of a strongly chordal graph. Secondly, we show that the query implication problem (Q\sb1\ \to\ Q\sb2) on two queries, which is to determine whether the data retrieved by query Q\sb1 is always a subset of the data retrieved by query Q\sb2, is not even in NP and in fact complete in \Pi\sb2\sp{p}. We present several \u27fine-grain\u27 analyses of the query implication problem and show that the query implication can be solved in polynomial time given chordal queries. Thirdly, we develop efficient parallel algorithms for manipulating directed hypergraphs H such as finding a directed path in H, closure of H, and minimum equivalent hypergraph of H. We show that finding a directed path in a directed hypergraph is inherently sequential. For directed hypergraphs with fixed degree and diameter we present NC algorithms for manipulations. Directed hypergraphs are representation schemes for functional dependencies in relational databases. Finally, we also present an efficient parallel algorithm for multi-dimensional range search. We show that a set of points in a rectangular parallelepiped can be obtained in O(logn) time with only 2.log\sp2 n $-$ 10.logn + 14 processors on a EREW-PRAM. A nontrivial implementation technique on the hypercube parallel architecture is also presented. Our method can be easily generalized to the case of d-dimensional range search

Connected Dominating Set Based Topology Control in Wireless Sensor Networks

Wireless Sensor Networks (WSNs) are now widely used for monitoring and controlling of systems where human intervention is not desirable or possible. Connected Dominating Sets (CDSs) based topology control in WSNs is one kind of hierarchical method to ensure sufficient coverage while reducing redundant connections in a relatively crowded network. Moreover, Minimum-sized Connected Dominating Set (MCDS) has become a well-known approach for constructing a Virtual Backbone (VB) to alleviate the broadcasting storm for efficient routing in WSNs extensively. However, no work considers the load-balance factor of CDSsin WSNs. In this dissertation, we first propose a new concept — the Load-Balanced CDS (LBCDS) and a new problem — the Load-Balanced Allocate Dominatee (LBAD) problem. Consequently, we propose a two-phase method to solve LBCDS and LBAD one by one and a one-phase Genetic Algorithm (GA) to solve the problems simultaneously. Secondly, since there is no performance ratio analysis in previously mentioned work, three problems are investigated and analyzed later. To be specific, the MinMax Degree Maximal Independent Set (MDMIS) problem, the Load-Balanced Virtual Backbone (LBVB) problem, and the MinMax Valid-Degree non Backbone node Allocation (MVBA) problem. Approximation algorithms and comprehensive theoretical analysis of the approximation factors are presented in the dissertation. On the other hand, in the current related literature, networks are deterministic where two nodes are assumed either connected or disconnected. In most real applications, however, there are many intermittently connected wireless links called lossy links, which only provide probabilistic connectivity. For WSNs with lossy links, we propose a Stochastic Network Model (SNM). Under this model, we measure the quality of CDSs using CDS reliability. In this dissertation, we construct an MCDS while its reliability is above a preset applicationspecified threshold, called Reliable MCDS (RMCDS). We propose a novel Genetic Algorithm (GA) with immigrant schemes called RMCDS-GA to solve the RMCDS problem. Finally, we apply the constructed LBCDS to a practical application under the realistic SNM model, namely data aggregation. To be specific, a new problem, Load-Balanced Data Aggregation Tree (LBDAT), is introduced finally. Our simulation results show that the proposed algorithms outperform the existing state-of-the-art approaches significantly

Algorithms and Generalizations for the Lovasz Local Lemma

The Lovasz Local Lemma (LLL) is a cornerstone principle of the probabilistic method for combinatorics. This shows that one can avoid a large of set of “bad-events” (forbidden configurations of variables), provided the local conditions are satisfied. The original probabilistic formulation of this principle did not give efficient algorithms. A breakthrough result of Moser & Tardos led to an framework based on resampling variables which turns nearly all applications of the LLL into efficient algorithms. We extend and generalize the algorithm of Moser & Tardos in a variety of ways. We show tighter bounds on the complexity of the Moser-Tardos algorithm, particularly its parallel form. We also give a new, faster parallel algorithm for the LLL. We show that in some cases, the Moser-Tardos algorithm can converge even thoughthe LLL itself does not apply; we give a new criterion (comparable to the LLL) for determining when this occurs. This leads to improved bounds for k-SAT and hypergraph coloring among other applications. We describe an extension of the Moser-Tardos algorithm based on partial resampling, and use this to obtain better bounds for problems involving sums of independent random variables, such as column-sparse packing and packet-routing. We describe a variant of the partial resampling algorithm specialized to approximating column-sparse covering integer programs, a generalization of set-cover. We also give hardness reductions and integrality gaps, showing that our partial resampling based algorithm obtains nearly optimal approximation factors. We give a variant of the Moser-Tardos algorithm for random permutations, one of the few cases of the LLL not covered by the original algorithm of Moser & Tardos. We use this to develop the first constructive algorithms for Latin transversals and hypergraph packing, including parallel algorithms. We analyze the distribution of variables induced by the Moser-Tardos algorithm. We show it has a random-like structure, which can be used to accelerate the Moser-Tardos algorithm itself as well as to cover problems such as MAX k-SAT in which we only partially avoid bad-events

Compressive sensing for signal ensembles

Compressive sensing (CS) is a new approach to simultaneous sensing and compression that enables a potentially large reduction in the sampling and computation costs for acquisition of signals having a sparse or compressible representation in some basis. The CS literature has focused almost exclusively on problems involving single signals in one or two dimensions. However, many important applications involve distributed networks or arrays of sensors. In other applications, the signal is inherently multidimensional and sensed progressively along a subset of its dimensions; examples include hyperspectral imaging and video acquisition. Initial work proposed joint sparsity models for signal ensembles that exploit both intra- and inter-signal correlation structures. Joint sparsity models enable a reduction in the total number of compressive measurements required by CS through the use of specially tailored recovery algorithms. This thesis reviews several different models for sparsity and compressibility of signal ensembles and multidimensional signals and proposes practical CS measurement schemes for these settings. For joint sparsity models, we evaluate the minimum number of measurements required under a recovery algorithm with combinatorial complexity. We also propose a framework for CS that uses a union-of-subspaces signal model. This framework leverages the structure present in certain sparse signals and can exploit both intra- and inter-signal correlations in signal ensembles. We formulate signal recovery algorithms that employ these new models to enable a reduction in the number of measurements required. Additionally, we propose the use of Kronecker product matrices as sparsity or compressibility bases for signal ensembles and multidimensional signals to jointly model all types of correlation present in the signal when each type of correlation can be expressed using sparsity. We compare the performance of standard global measurement ensembles, which act on all of the signal samples; partitioned measurements, which act on a partition of the signal with a given measurement depending only on a piece of the signal; and Kronecker product measurements, which can be implemented in distributed measurement settings. The Kronecker product formulation in the sparsity and measurement settings enables the derivation of analytical bounds for transform coding compression of signal ensembles and multidimensional signals. We also provide new theoretical results for performance of CS recovery when Kronecker product matrices are used, which in turn motivates new design criteria for distributed CS measurement schemes