The Costas-array problem is a combinatorial constraint-satisfaction problem (CSP) that remains unsolved for many array sizes greater than 30. In order to reduce the time required to solve large instances, we present an Ant Colony Optimization algorithm called m-Dimensional Relative Ant Colony Optimization (mDRACO) for combinatorial CSPs, focusing specifically on the Costas-array problem. This paper introduces the optimizations included in mDRACO, such as map-based association of pheromone with arbitrary-length component sequences and relative path storage. We assess the quality of the resulting mDRACO framework on the Costas-array problem by computing the efficiency of its processor utilization and comparing its run time to that of an ACO framework without the new optimizations. mDRACO gives promising results; it has efficiency greater than 0.5 and reduces time-to-first-solution for the m = 16 Costas-array problem by a factor of over 300.
The Costas-array problem is a combinatorial constraint-satisfaction problem (CSP) that remains unsolved for many array sizes greater than 30. In order to reduce the time required to solve large instances, we present an Ant Colony Optimization algorithm called m-Dimensional Relative Ant Colony Optimization ($$m$$ m DRACO) for combinatorial CSPs, focusing specifically on the Costas-array problem. This paper introduces the optimizations included in $$m$$ m DRACO, such as map-based association of pheromone with arbitrary-length component sequences and relative path storage. We assess the quality of the resulting $$m$$ m DRACO framework on the Costas-array problem by computing the efficiency of its processor utilization and comparing its run time to that of an ACO framework without the new optimizations. $$m$$ m DRACO gives promising results; it has efficiency greater than 0.5 and reduces time-to-first-solution for the $$m = 16$$ m = 16 Costas-array problem by a factor of over 300.
The importance of classifying connections in large graphs has been the motivation for a rich line of work on distributed subgraph finding that has led to exciting recent breakthroughs. A crucial aspect that remained open was whether deterministic algorithms can be as efficient as their randomized counterparts, where the latter are known to be tight up to polylogarithmic factors.We give deterministic distributed algorithms for listing cliques of size 𝑝 in 𝑛 1−2/𝑝+𝑜 (1) rounds in the Congest model. For triangles, our 𝑛 1/3+𝑜 (1) round complexity improves upon the previous state of the art of 𝑛 2/3+𝑜 (1) rounds [Chang and Saranurak, FOCS 2020]. For cliques of size 𝑝 ≥ 4, ours are the first non-trivial deterministic distributed algorithms. Given known lower bounds, for all values 𝑝 ≥ 3 our algorithms are tight up to a 𝑛 𝑜 (1) subpolynomial factor, which comes from the deterministic routing procedure we use. CCS CONCEPTS• Theory of computation → Distributed algorithms.
In an extant population, how much information do extant individuals provide on the pedigree of their ancestors? Recent work by Kim, Mossel, Ramnarayan and Turner (2020) studied this question under a number of simplifying assumptions, including random mating, fixed length inheritance blocks and sufficiently large founding population. They showed that under these conditions if the average number of offspring is a sufficiently large constant, then it is possible to recover a large fraction of the pedigree structure and genetic content by an algorithm they named REC-GEN.We are interested in studying the performance of REC-GEN on simulated data generated according to the model. As a first step, we improve the running time of the algorithm. However, we observe that even the faster version of the algorithm does not do well in any simulations in recovering the pedigree beyond 2 generations. We claim that this is due to the inbreeding present in any setting where the algorithm can be run, even on simulated data. To support the claim we show that a main step of the algorithm, called ancestral reconstruction, performs accurately in an idealized setting with no inbreeding but performs poorly in random mating populations.To overcome the poor behavior of REC-GEN we introduce a Belief-Propagation based heuristic that accounts for the inbreeding and performs much better in our simulations.
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