Finding Optimal 2-Packing Sets on Arbitrary Graphs at Scale

A 2-packing set for an undirected graph $G=(V,E)$ is a subset $\mathcal{S} \subset V$ such that any two vertices $v_1,v_2 \in \mathcal{S}$ have no common neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem. We develop a new approach to solve this problem on arbitrary graphs using its close relation to the independent set problem. Thereby, our algorithm red2pack uses new data reduction rules specific to the 2-packing set problem as well as a graph transformation. Our experiments show that we outperform the state-of-the-art for arbitrary graphs with respect to solution quality and also are able to compute solutions multiple orders of magnitude faster than previously possible. For example, we are able to solve 63% of our graphs to optimality in less than a second while the competitor for arbitrary graphs can only solve 5% of the graphs in the data set to optimality even with a 10 hour time limit. Moreover, our approach can solve a wide range of large instances that have previously been unsolved

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

From in vitro evolution to protein structure

In the nanoscale, the machinery of life is mainly composed by macromolecules and macromolecular complexes that through their shapes create a network of interconnected mechanisms of biological processes. The relationship between shape and function of a biological molecule is the foundation of structural biology, that aims at studying the structure of a protein or a macromolecular complex to unveil the molecular mechanism through which it exerts its function. What about the reverse: is it possible by exploiting the function for which a protein was naturally selected to deduce the protein structure? To this aim we developed a method, called CAMELS (Coupling Analysis by Molecular Evolution Library Sequencing), able to obtain the structural features of a protein from an artificial selection based on that protein function. With CAMELS we tried to reconstruct the TEM-1 beta lactamase fold exclusively by generating and sequencing large libraries of mutational variants. Theoretically with this method it is possible to reconstruct the structure of a protein regardless of the species of origin or the phylogenetical time of emergence when a functional phenotypic selection of a protein is available. CAMELS allows us to obtain protein structures without needing to purify the protein beforehand