We study Crystal Structure Prediction, one of the major problems in computational chemistry. This is essentially a continuous optimization problem, where many different, simple and sophisticated, methods have been proposed and applied. The simple searching techniques are easy to understand, usually easy to implement, but they can be slow in practice. On the other hand, the more sophisticated approaches perform well in general, however almost all of them have a large number of parameters that require fine tuning and, in the majority of the cases, chemical expertise is needed in order to properly set them up. In addition, due to the chemical expertise involved in the parameter-tuning, these approaches can be biased towards previously-known crystal structures. Our contribution is twofold. Firstly, we formalize the Crystal Structure Prediction problem, alongside several other intermediate problems, from a theoretical computer science perspective. Secondly, we propose an oblivious algorithm for Crystal Structure Prediction that is based on local search. Oblivious means that our algorithm requires minimal knowledge about the composition we are trying to compute a crystal structure for. In addition, our algorithm can be used as an intermediate step by any method. Our experiments show that our algorithms outperform the standard basin hopping, a well studied algorithm for the problem.  

In this work, we consider adversarial crash faults of nodes in the network constructors model [Michail and Spirakis, 2016]. We first show that, without further assumptions, the class of graph languages that can be (stably) constructed under crash faults is nonempty but small. In particular, if an unbounded number of crash faults may occur, we prove that (i) the only constructible graph language is that of spanning cliques and (ii) a strong impossibility result holds even if the size of the graphs that the protocol outputs in populations of size n need only grow with n (the remaining nodes being waste). When there is a finite upper bound f on the number of faults, we show that it is impossible to construct any non-hereditary graph language and leave as an interesting open problem the hereditary case. On the positive side, by relaxing our requirements we prove that: (i) permitting linear waste enables to construct on n/(2f) − f nodes, any graph language that is constructible in the fault-free case, (ii) partial constructibility (i.e., not having to generate all graphs in the language) allows the construction of a large class of graph languages. We then extend the original model with a minimal form of fault notifications. Our main result here is a fault-tolerant universal constructor : We develop a fault-tolerant protocol for spanning line and use it to simulate a linear-space Turing Machine M. This allows a fault-tolerant construction of any graph accepted by M in linear space, with waste min{n/2 + f(n), n}, where f(n) is the number of faults in the execution. We then prove that increasing the permissible waste to min{2n/3+f(n), n} allows the construction of graphs accepted by an O(n^2)-space Turing Machine, which is asymptotically the maximum simulation space that we can hope for in this model. Finally, we show that logarithmic local memories can be exploited for a no-waste faulttolerant simulation of any such protocol.   Cite paper:

@inproceedings{michail2019fault,
  title={Fault tolerant network constructors},
  author={Michail, Othon and Spirakis, Paul G and Theofilatos, Michail},
  booktitle={International Symposium on Stabilizing, Safety, and Security of Distributed Systems},
  pages={243--255},
  year={2019},
  organization={Springer}
}

We study population protocols: networks of anonymous agents whose pairwise interactions are chosen uniformly at random. The size counting problem is that of calculating the exact number n of agents in the population, assuming no leader (each agent starts in the same state). We give the first protocol that solves this problem in sublinear time. The protocol converges in O(log n log log n) time and uses O(n^60) states (O(1)+60 log n bits of memory per agent) with probability 1−O((log log n)/n). The time to converge is also O(log n log log n) in expectation. Crucially, unlike most published protocols with ω(1) states, our protocol is uniform: it uses the same transition algorithm for any population size, so does not need an estimate of the population size to be embedded into the algorithm. A sub protocol is the first uniform sublinear-time leader election population protocol, taking O(log n log log n) time and O(n^18) states. The state complexity of both the counting and leader election protocols can be reduced to O(n^30) and O(n^9) respectively, while increasing the time to O(log^2 n).   Cite paper:

@article{doty2018brief,
  title={Brief announcement: Exact size counting in uniform population protocols in nearly logarithmic time},
  author={Doty, David and Eftekhari, Mahsa and Michail, Othon and Spirakis, Paul G and Theofilatos, Michail},
  journal={Leibniz International Proceedings in Informatics, LIPIcs},
  volume={121},
  year={2018}
}

We study the problems of leader election and population size counting for population protocols: networks of finite-state anonymous agents that interact randomly under a uniform random scheduler. We provide simple protocols for approximate counting of the size of the population and for leader election. We show a protocol for leader election that terminates in O(log^2(n)/log(m)) parallel time, where 1 ≤ m ≤ n is a parameter, using O(max{m, log n}) states. By adjusting the parameter m between a constant and n, we obtain a single leader election protocol whose time and space can be smoothly traded off between O(log^2(n)) to O(log n) time and O(log n) to O(n) states. We also give a protocol which provides an upper bound n’ of the size n of the population, where n’ is at most n a for some constant a > 1. This protocol assumes the existence of a unique leader in the population and stabilizes in Θ(log n) parallel time, using constant number of states in every node, except from the unique leader which is required to use Θ(log^2(n)) states.   Cite paper:

@inproceedings{michail2018simple,
  title={Simple and fast approximate counting and leader election in populations},
  author={Michail, Othon and Spirakis, Paul G and Theofilatos, Michail},
  booktitle={International Symposium on Stabilizing, Safety, and Security of Distributed Systems},
  pages={154--169},
  year={2018},
  organization={Springer}
}