Beeping a Deterministic Time-Optimal Leader Election

The beeping model is an extremely restrictive broadcast communication model that relies only on carrier sensing. In this model, we solve the leader election problem with an asymptotically optimal round complexity of O(D + log n), for a network of unknown size n and unknown diameter D (but with unique identifiers). Contrary to the best previously known algorithms in the same setting, the proposed one is deterministic. The techniques we introduce give a new insight as to how local constraints on the exchangeable messages can result in efficient algorithms, when dealing with the beeping model. Using this deterministic leader election algorithm, we obtain a randomized leader election algorithm for anonymous networks with an asymptotically optimal round complexity of O(D + log n) w.h.p. In previous works this complexity was obtained in expectation only. Moreover, using deterministic leader election, we obtain efficient algorithms for symmetry-breaking and communication procedures: O(log n) time MIS and 5-coloring for tree networks (which is time-optimal), as well as k-source multi-broadcast for general graphs in O(min(k,log n) * D + k log{(n M)/k}) rounds (for messages in {1,..., M}). This latter result improves on previous solutions when the number of sources k is sublogarithmic (k = o(log n))

Monte Carlo Tree Search for Feature Model Analyses: a General Framework for Decision-Making

The colossal solution spaces of most configurable systems make intractable their exhaustive exploration. Accordingly, relevant anal-yses remain open research problems. There exist analyses alterna-tives such as SAT solving or constraint programming. However, none of them have explored simulation-based methods. Monte Carlo-based decision making is a simulation based method for deal-ing with colossal solution spaces using randomness. This paper proposes a conceptual framework that tackles various of those anal-yses using Monte Carlo methods, which have proven to succeed in vast search spaces (e.g., game theory). Our general framework is described formally, and its flexibility to cope with a diversity of analysis problemsis discussed (e.g., finding defective configurations, feature model reverse engineering or getting optimal performance configurations). Additionally, we present a Python implementation of the framework that shows the feasibility of our proposal. With this contribution, we envision that different problems can be ad dressed using Monte Carlo simulations and that our framework can be used to advance the state of the art a step forward.Ministerio de Economía y Competitividad RTI2018-101204-B-C22 (OPHELIA

FPTAS for Weighted Fibonacci Gates and Its Applications

Fibonacci gate problems have severed as computation primitives to solve other problems by holographic algorithm and play an important role in the dichotomy of exact counting for Holant and CSP frameworks. We generalize them to weighted cases and allow each vertex function to have different parameters, which is a much boarder family and #P-hard for exactly counting. We design a fully polynomial-time approximation scheme (FPTAS) for this generalization by correlation decay technique. This is the first deterministic FPTAS for approximate counting in the general Holant framework without a degree bound. We also formally introduce holographic reduction in the study of approximate counting and these weighted Fibonacci gate problems serve as computation primitives for approximate counting. Under holographic reduction, we obtain FPTAS for other Holant problems and spin problems. One important application is developing an FPTAS for a large range of ferromagnetic two-state spin systems. This is the first deterministic FPTAS in the ferromagnetic range for two-state spin systems without a degree bound. Besides these algorithms, we also develop several new tools and techniques to establish the correlation decay property, which are applicable in other problems