HP-SFC Algorithm for MmWave Massive MIMO Hybrid Precoding Systems

This paper presents an alternating iteration hybrid precoding algorithm for the switch network-based dynamic fully-connected (SFC) structure, namely HP-SFC algorithm. Firstly, based on the sparsity of switch network, the optimization problem of the analog switch precoding matrix is transformed into a binary dictionary updating problem, which avoids to deal with the binary constraint straightly. Then, the optimization problem of the analog phase shifter (PS) precoding matrix is modeled as a quadratic unimodular programming problem by the vectorization of the analog PS precoding matrix. So that the analog PS precoding matrix can be readily optimized. Finally, the analog switch precoding matrix, the analog PS precoding matrix and the digital precoding matrix are alternately optimized via the block coordinate descent, the generalized power method and the least square, respectively. Theoretical analysis and simulation results show that the proposed algorithm can provide brilliantly hybrid precoding performence campared with the previous works, for example: 1) it reduces the hybrid precoding matrix residual, so that its spectral efficiency is close to the full digital optimal precoding; 2) it provids at least 15\% energy efficiency improvement comparing with related algorithms.

Graph Neural Networks for Maximum Constraint Satisfaction

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for all binary constraint satisfaction problems. Training is unsupervised, and it is sufficient to train on relatively small instances; the resulting networks perform well on much larger instances (at least 10-times larger). We experimentally evaluate our approach for a variety of problems, including Maximum Cut and Maximum Independent Set. Despite being generic, we show that our approach matches or surpasses most greedy and semi-definite programming based algorithms and sometimes even outperforms state-of-the-art heuristics for the specific problems.

Galois Connections for Patterns: An Algebra of Labelled Graphs

A pattern is a generic instance of a binary constraint satisfaction problem (CSP) in which the compatibility of certain pairs of variable-value assignments may be unspecified. The notion of forbidden pattern has led to the discovery of several novel tractable classes for the CSP. However, for this field to come of age it is time for a theoretical study of the algebra of patterns. We present a Galois connection between lattices composed of sets of forbidden patterns and sets of generic instances, and investigate its consequences. We then extend patterns to augmented patterns and exhibit a similar Galois connection. Augmented patterns are a more powerful language than flat (i.e. non-augmented) patterns, as we demonstrate by showing that, for any $$k \ge 1$$ k ≥ 1 , instances with tree-width bounded by k cannot be specified by forbidding a finite set of flat patterns but can be specified by a finite set of augmented patterns. A single finite set of augmented patterns can also describe the class of instances such that each instance has a weak near-unanimity polymorphism of arity k (thus covering all tractable language classes).We investigate the power of forbidding augmented patterns and discuss their potential for describing new tractable classes.

Interpretable and effective hashing via Bernoulli variational auto-encoders

Due to the rapid increase in the amount of data generated in many fields of science and engineering, information retrieval methods tailored to large-scale datasets have become increasingly important in the last years. Semantic hashing is an emerging technique for this purpose that works on the idea of representing complex data objects, like images and text, using similarity-preserving binary codes that are then used for indexing and search. In this paper, we investigate a hashing algorithm that uses a deep variational auto-encoder to learn and predict the codes. Unlike previous approaches of this type, that learn a continuous (Gaussian) representation and then project the embedding to obtain hash codes, our method employs Bernoulli latent variables in both the training and the prediction stage. Constraining the model to use a binary encoding allow us to obtain a more interpretable representation for hashing: each factor in the generative model represents a bit that should help to reconstruct and thus identify the input pattern. Interestingly, we found that the binary constraint does not lead to a loss but an increase of search accuracy. We argue that continuous formulations learn a representation that can significantly differ from the code used for search. Minding this gap in the design of the auto-encoder can translate into more accurate retrieval results. Extensive experiments on seven datasets involving image data and text data illustrate these findings and demonstrate the advantages of our approach.

Minimizing Cost Travel in Multimodal Transport Using Advanced Relation Transitive Closure

The optimization computation is an essential transversal branch of operations research which is primordial in many technical fields: transport, finance, networks, energy, learning, etc. In fact, it aims to minimize the resource consumption and maximize the generated profits. This work provides a new method for cost optimization which can be applied either on path optimization for graphs or on binary constraint reduction for Constraint Satisfaction Problem (CSP). It is about the computing of the “transitive closure of a given binary relation with respect to a property.” Thus, this paper introduces the mathematical background for the transitive closure of binary relations. Then, it gives the algorithms for computing the closure of a binary relation according to another one. The elaborated algorithms are shown to be polynomial. Since this technique is of great interest, we show its applications in some important industrial fields.

Solving Sudoku with Consistency: A Visual and Interactive Approach

We describe an online, interactive system with a graphical interface to illustrate the power and operation of consistency algorithms in a friendly and popular context, namely, solving Sudoku puzzles. Our tool implements algorithms for enforcing five (domain-based) consistency properties on binary and non-binary constraint models. Our tool is useful for research, education, and outreach. From a scientific standpoint, we propose a new consistency property that can solve the hardest known 9×9 Sudoku instances without search, but leave open the question of the lowest level of consistency needed to solve every 9×9 Sudoku puzzle. We have used the current tool and its predecessor in the classroom to introduce students to modeling problems with constraints, explain consistency properties, and illustrate the operations of constraint propagation and lookahead. Finally, we have also used this tool during outreach activities to demystify AI to children and the general public and show them how computers think.