A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

An Algorithm for Optimal Bipartite PLA Folding

This paper presents some results of PLA area optimizing by means of its column and row folding. A more restricted type of PLA simple folding is considered. It is introduced by Egan and Liu and called as bipartite folding. An efficient approach is presented which allows finding an optimal bipartite folding without exhaustive computational efforts

Pseudoknots in a Homopolymer

After a discussion of the definition and number of pseudoknots, we reconsider the self-attracting homopolymer paying particular attention to the scaling of the number of pseudoknots at different temperature regimes in two and three dimensions. Although the total number of pseudoknots is extensive at all temperatures, we find that the number of pseudoknots forming between the two halves of the chain diverges logarithmically at (in both dimensions) and below (in 2d only) the theta-temparature. We later introduce a simple model that is sensitive to pseudoknot formation during collapse. The resulting phase diagram involves swollen, branched and collapsed homopolymer phases with transitions between each pair.Comment: submitted to PR

Efficient Generation of Stable Planar Cages for Chemistry

In this paper we describe an algorithm which generates all colored planar maps with a good minimum sparsity from simple motifs and rules to connect them. An implementation of this algorithm is available and is used by chemists who want to quickly generate all sound molecules they can obtain by mixing some basic components.Comment: 17 pages, 7 figures. Accepted at the 14th International Symposium on Experimental Algorithms (SEA 2015

Application of Timber and Wood-based Materials in Architectural Design using Multi-objective Optimisation Tools

Digital fabrication leads architects and structural engineers to modify the design optimisation methodology. The designers, as never before, are facing new technologies developed in the search for new materials based, among others, on wood components and the improvement of manufacturing methods at the same time. In this process, the material and manufacturing technology adjustment to desired aesthetic outcomes is possible not only by the material used but also by the self-organisation of the structure's optimisation. New fabrication techniques linked with topology optimising software change traditional load-bearing systems designing using timber and wood-based materials. Multi-objective optimisation research indicates that timber might be a comprehensive material based on various applications from low-tech to cutting-edge contemporary fabrication technologies. The article presents new tools and methods for the optimisation of structural elements. A case study based on interdisciplinary architectural and structural optimisation suggests the possible effective research-based design. Comparing contemporary buildings with wood load-bearing structures explains timber usage's diversity and characteristics in modern design

Towards Effective Exact Algorithms for the Maximum Balanced Biclique Problem

The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP. Firstly, we introduce an Upper Bound Propagation procedure to pre-compute an upper bound involving each vertex. Then we extend an existing branch-and-bound algorithm by integrating the pre-computed upper bounds. We also present a set of new valid inequalities induced from the upper bounds to tighten an existing mathematical formulation for MBBP. Lastly, we investigate another exact algorithm scheme which enumerates a subset of balanced bicliques based on our upper bounds. Experiments show that compared to existing approaches, the proposed algorithms and formulations are more efficient in solving a set of random graphs and large real-life instances

Silicon compilation

Silicon compilation is a term used for many different purposes. In this paper we define silicon compilation as a mapping from some higher level description into layout. We define the basic issues in structural and behavioral silicon compilation and some possible solutions to those issues. Finally, we define the concept of an intelligent silicon compiler in which the compiler evaluates the quality of the generated design and attempts to improve it if it is not satisfactory