Consecutive ones matrices for multi-dimensional orthogonal packing problems

International audienceThe multi-dimensional orthogonal packing problem (OPP) is a well studied decisional problem. Given a set of items with rectangular shapes, the problem is to decide whether there is a non-overlapping packing of these items in a rectangular bin. The rotation of items is not allowed. A powerful caracterization of packing configurations by means of interval graphs was recently introduced. In this paper, we propose a new algorithm using consecutive ones matrices as data structure. This new algorithm is then used to solve the two-dimensional orthogonal knapsack problem. Computational results are reported, which show its effectiveness

Multiuser Diversity for Secrecy Communications Using Opportunistic Jammer Selection -- Secure DoF and Jammer Scaling Law

In this paper, we propose opportunistic jammer selection in a wireless security system for increasing the secure degrees of freedom (DoF) between a transmitter and a legitimate receiver (say, Alice and Bob). There is a jammer group consisting of $S$ jammers among which Bob selects $K$ jammers. The selected jammers transmit independent and identically distributed Gaussian signals to hinder the eavesdropper (Eve). Since the channels of Bob and Eve are independent, we can select the jammers whose jamming channels are aligned at Bob, but not at Eve. As a result, Eve cannot obtain any DoF unless it has more than $KN_j$ receive antennas, where $N_j$ is the number of jammer's transmit antenna each, and hence $KN_j$ can be regarded as defensible dimensions against Eve. For the jamming signal alignment at Bob, we propose two opportunistic jammer selection schemes and find the scaling law of the required number of jammers for target secure DoF by a geometrical interpretation of the received signals.Comment: Accepted with minor revisions, IEEE Trans. on Signal Processin

Non-Euclidean geometry in nature

I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random graphs. For these systems I discuss the following interlinked questions: (i) the optimal embedding of plants leaves in the three-dimensional space, (ii) the spectral statistics of sparse random matrix ensembles.Comment: 52 pages, 21 figures, last section is rewritten, a reference to chaotic Hamiltonian systems is adde

Precoder Design for Physical Layer Multicasting

This paper studies the instantaneous rate maximization and the weighted sum delay minimization problems over a K-user multicast channel, where multiple antennas are available at the transmitter as well as at all the receivers. Motivated by the degree of freedom optimality and the simplicity offered by linear precoding schemes, we consider the design of linear precoders using the aforementioned two criteria. We first consider the scenario wherein the linear precoder can be any complex-valued matrix subject to rank and power constraints. We propose cyclic alternating ascent based precoder design algorithms and establish their convergence to respective stationary points. Simulation results reveal that our proposed algorithms considerably outperform known competing solutions. We then consider a scenario in which the linear precoder can be formed by selecting and concatenating precoders from a given finite codebook of precoding matrices, subject to rank and power constraints. We show that under this scenario, the instantaneous rate maximization problem is equivalent to a robust submodular maximization problem which is strongly NP hard. We propose a deterministic approximation algorithm and show that it yields a bicriteria approximation. For the weighted sum delay minimization problem we propose a simple deterministic greedy algorithm, which at each step entails approximately maximizing a submodular set function subject to multiple knapsack constraints, and establish its performance guarantee.Comment: 37 pages, 8 figures, submitted to IEEE Trans. Signal Pro

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Carbon--The First Frontier of Information Processing

Information is often encoded as an aperiodic chain of building blocks. Modern digital computers use bits as the building blocks, but in general the choice of building blocks depends on the nature of the information to be encoded. What are the optimal building blocks to encode structural information? This can be analysed by substituting the operations of addition and multiplication of conventional arithmetic with translation and rotation. It is argued that at the molecular level, the best component for encoding discretised structural information is carbon. Living organisms discovered this billions of years ago, and used carbon as the back-bone for constructing proteins that function according to their structure. Structural analysis of polypeptide chains shows that an efficient and versatile structural language of 20 building blocks is needed to implement all the tasks carried out by proteins. Properties of amino acids indicate that the present triplet genetic code was preceded by a more primitive one, coding for 10 amino acids using two nucleotide bases.Comment: (v1) 9 pages, revtex. (v2) 10 pages. Several arguments expanded to make the article self-contained and to increase clarity. Applications pointed out. (v3) 11 pages. Published version. Well-known properties of proteins shifted to an appendix. Reformatted according to journal styl