Polynomial tuning of multiparametric combinatorial samplers

Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like structures. In their multiparametric variants, these samplers allow to control the profile of expected values corresponding to multiple combinatorial parameters. One can control, for instance, the number of leaves, profile of node degrees in trees or the number of certain subpatterns in strings. However, such a flexible control requires an additional non-trivial tuning procedure. In this paper, we propose an efficient polynomial-time, with respect to the number of tuned parameters, tuning algorithm based on convex optimisation techniques. Finally, we illustrate the efficiency of our approach using several applications of rational, algebraic and P\'olya structures including polyomino tilings with prescribed tile frequencies, planar trees with a given specific node degree distribution, and weighted partitions.Comment: Extended abstract, accepted to ANALCO2018. 20 pages, 6 figures, colours. Implementation and examples are available at [1] https://github.com/maciej-bendkowski/boltzmann-brain [2] https://github.com/maciej-bendkowski/multiparametric-combinatorial-sampler

On the enumeration of closures and environments with an application to random generation

Environments and closures are two of the main ingredients of evaluation in lambda-calculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In this paper we investigate some dynamic aspects of evaluation in lambda-calculus considering the quantitative, combinatorial properties of environments and closures. Focusing on two classes of environments and closures, namely the so-called plain and closed ones, we consider the problem of their asymptotic counting and effective random generation. We provide an asymptotic approximation of the number of both plain environments and closures of size $n$. Using the associated generating functions, we construct effective samplers for both classes of combinatorial structures. Finally, we discuss the related problem of asymptotic counting and random generation of closed environemnts and closures

Subcritical graph classes containing all planar graphs

We construct minor-closed addable families of graphs that are subcritical and contain all planar graphs. This contradicts (one direction of) a well-known conjecture of Noy

Finding Shortest Path using Dijkstra in Live Traffic Simuation

These days, a few online administrations give live activity information, for example, Google-Map, Navteq , INRIX Traffic Information Provider , and TomTom NV. Yet at the same time figuring the most limited way on live movement is enormous issue. This is critical for auto route as it helps drivers to decide. In displayed approach server will gather live activity data and afterward declare them over remote system. With this approach any number of customers can be included. This new approach called live movement file time dependant (LTI-TD) empowers drivers to upgrade their briefest way come about by accepting just a little division of the file. The current frameworks were infeasible to tackle the issue because of their restrictive upkeep time and extensive transmission overhead. LTI-TD is a novel answer for Online Shortest Path Computation on Time Dependent Network

Finding Shortest Path using Dijkstra in Live Traffic Simuation

These days, a few online administrations give live activity information, for example, Google-Map, Navteq , INRIX Traffic Information Provider , and TomTom NV. Yet at the same time figuring the most limited way on live movement is enormous issue. This is critical for auto route as it helps drivers to decide. In displayed approach server will gather live activity data and afterward declare them over remote system. With this approach any number of customers can be included. This new approach called live movement file time dependant (LTI-TD) empowers drivers to upgrade their briefest way come about by accepting just a little division of the file. The current frameworks were infeasible to tackle the issue because of their restrictive upkeep time and extensive transmission overhead. LTI-TD is a novel answer for Online Shortest Path Computation on Time Dependent Network

Finding Shortest Path using Dijkstra in Live Traffic Simuation

These days, a few online administrations give live activity information, for example, Google-Map, Navteq , INRIX Traffic Information Provider , and TomTom NV. Yet at the same time figuring the most limited way on live movement is enormous issue. This is critical for auto route as it helps drivers to decide. In displayed approach server will gather live activity data and afterward declare them over remote system. With this approach any number of customers can be included. This new approach called live movement file time dependant (LTI-TD) empowers drivers to upgrade their briefest way come about by accepting just a little division of the file. The current frameworks were infeasible to tackle the issue because of their restrictive upkeep time and extensive transmission overhead. LTI-TD is a novel answer for Online Shortest Path Computation on Time Dependent Network