"The maximum density still life problem (MDSLP) is a hard constraint optimization problem based on Conway's game of life. It is a prime example of weighted constrained optimization problem that has been recently tackled in the constraint-programming community. Bucket elimination (BE) is a complete technique commonly used to solve this kind of constraint satisfaction problem. When the memory required to apply BE is too high, a heuristic method based on it (denominated mini-buckets) can be used to calculate bounds for the optimal solution. Nevertheless, the curse of dimensionality makes these techniques unpractical for large size problems. In response to this situation, we present a memetic algorithm for the MDSLP in which BE is used as a mechanism for recombining solutions, providing the best possible child from the parental set. Subsequently, a multi-level model in which this exact/metaheuristic hybrid is further hybridized with branch-and-bound techniques and mini-buckets is studied. Extensive experimental results analyze the performance of these models and multi-parent recombination. The resulting algorithm consistently finds optimal patterns for up to date solved instances in less time than current approaches. Moreover, it is shown that this proposal provides new best known solutions for very large instances."

things I never learned

"In this paper, we study the consensus problem of multiple agents on a kind of famous graph, Peterson graph. It is an undirected graph with 10 vertices and 15 edges. Each agent randomly walks on this graph and communicates with each other if and only if they coincide on a node at the same time. We conduct numerical study on the consensus problem in this framework and show that global consensus can be achieved."

"The B36/S125 (or "2x2") cellular automaton is one that takes place on a 2D square lattice much like Conway's Game of Life. Although it exhibits high-level behaviour that is similar to Life, such as chaotic but eventually stable evolution and the existence of a natural diagonal glider, the individual objects that the rule contains generally look very different from their Life counterparts. In this article, a history of notable discoveries in the 2x2 rule is provided, and the fundamental patterns of the automaton are described. Some theoretical results are derived along the way, including a proof that the speed limits for diagonal and orthogonal spaceships in this rule are c/3 and c/2, respectively. A Margolus block cellular automaton that 2x2 emulates is investigated, and in particular a family of oscillators made up entirely of 2 x 2 blocks are analyzed and used to show that there exist oscillators with period 2^m(2^k - 1) for any integers m,k geq 1."

In this paper, we obtain polynomial time algorithms to determine the acyclic chromatic number, the star chromatic number, the Thue chromatic number, the harmonious chromatic number and the clique chromatic number of $P_4$-tidy graphs and $(q,q-4)$-graphs, for every fixed $q$. These classes include cographs, $P_4$-sparse and $P_4$-lite graphs. All these coloring problems are known to be NP-hard for general graphs. These algorithms are fixed parameter tractable on the parameter $q(G)$, which is the minimum $q$ such that $G$ is a $(q,q-4)$-graph. We also prove that every connected $(q,q-4)$-graph with at least $q$ vertices is 2-clique-colorable and that every acyclic coloring of a cograph is also nonrepetitive.

"Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as species enter an ecosystem via migration or speciation, and leave via extinction.

In a previous paper, a complexity measure of networks was proposed based on the {em complexity is information content} paradigm. To apply this paradigm to any object, one must fix two things: a representation language, in which strings of symbols from some alphabet describe, or stand for the objects being considered; and a means of determining when two such descriptions refer to the same object. With these two things set, the information content of an object can be computed in principle from the number of equivalent descriptions describing a particular object.

The previously proposed representation language had the deficiency that the fully connected and empty networks were the most complex for a given number of nodes. A variation of this measure, called zcomplexity, applied a compression algorithm to the resulting bitstring representation, to solve this problem. Unfortunately, zcomplexity proved too computationally expensive to be practical.
In this paper, I propose a new representation language that encodes the number of links along with the number of nodes and a representation of the linklist. This, like zcomplexity, exhibits minimal complexity for fully connected and empty networks, but is as tractable as the original measure."

"Consider a large Boolean network with a feed forward structure. Given a probability distribution for the inputs, can one find-possibly small-collections of input nodes that determine the states of most other nodes in the network?…"

"While magic squares have been known and studied for many centuries, it is surprising that for certain types of magic squares we still do not know today which are the smallest possible! In an effort to make progress on these unsolved problems, twelve prizes totaling €8,000 and 12 bottles of champagne are offered for the solutions to twelve enigmas (six main at €1,000 each, six small from €100 to €500 each):…"

"Motivation: Second generation sequencing technology makes it feasible for many researches to obtain enough sequence reads to attempt the de novo assembly of higher eukaryotes (including mammals). De novo assembly not only provides a tool for understanding wide scale biological variation, but within human bio-medicine, it offers a direct way of observing both large scale structural variation and fine scale sequence variation. Unfortunately, improvements in the computational feasibility for de novo assembly have not matched the improvements in the gathering of sequence data. This is for two reasons: the inherent computational complexity of the problem, and the in-practice memory requirements of tools."

"Many functions have been recently defined to assess the similarity among networks as tools for quantitative comparison. They stem from very different frameworks - and they are tuned for dealing with different situations. Here we show an overview of the spectral distances, highlighting their behavior in some basic cases of static and dynamic synthetic and real networks."

"The China Labyrinth was conceived in the early eighties by Martin Medema who was first to imagine 64 hexagons in a configuration wherein each would differ from all others in terms of the configuration of neighbours around it. That was brilliant."

"The purpose of this site is to try to provide information on the various polyforms: poly-ominoes, -iamonds, -hexes, -cubes etc. There is a great deal of information already on the internet and these pages will try to provide links to all (well hopefully most!) relevant sites. Where no information seems available elsewhere as much information as possible will be posted here."

"After a bit of work we believe we have solved most of the practical problems that have to be taken care of before starting a free journal. This is probably the easy part. Now we have to decide if it is a good idea or not.

The aim is to have a high quality journal for the CG community that is run by the CG community and free to everyone (really free, no cost to publish and no cost to access). Obviously such a journal needs the support of the CG community to be successful. The work should be shared among the community, i.e., the editorial board and editorial manager(s) should be replaced regularly. "