Perfect sampling algorithm for Schur processes

We describe random generation algorithms for a large class of random combinatorial objects called Schur processes, which are sequences of random (integer) partitions subject to certain interlacing conditions. This class contains several fundamental combinatorial objects as special cases, such as plane partitions, tilings of Aztec diamonds, pyramid partitions and more generally steep domino tilings of the plane. Our algorithm, which is of polynomial complexity, is both exact (i.e. the output follows exactly the target probability law, which is either Boltzmann or uniform in our case), and entropy optimal (i.e. it reads a minimal number of random bits as an input). The algorithm encompasses previous growth procedures for special Schur processes related to the primal and dual RSK algorithm, as well as the famous domino shuffling algorithm for domino tilings of the Aztec diamond. It can be easily adapted to deal with symmetric Schur processes and general Schur processes involving infinitely many parameters. It is more concrete and easier to implement than Borodin's algorithm, and it is entropy optimal. At a technical level, it relies on unified bijective proofs of the different types of Cauchy and Littlewood identities for Schur functions, and on an adaptation of Fomin's growth diagram description of the RSK algorithm to that setting. Simulations performed with this algorithm suggest interesting limit shape phenomena for the corresponding tiling models, some of which are new.Comment: 26 pages, 19 figures (v3: final version, corrected a few misprints present in v2

Rate-distortion and complexity optimized motion estimation for H.264 video coding

11.264 video coding standard supports several inter-prediction coding modes that use macroblock (MB) partitions with variable block sizes. Rate-distortion (R-D) optimal selection of both the motion vectors (MVs) and the coding mode of each MB is essential for an H.264 encoder to achieve superior coding efficiency. Unfortunately, searching for optimal MVs of each possible subblock incurs a heavy computational cost. In this paper, in order to reduce the computational burden of integer-pel motion estimation (ME) without sacrificing from the coding performance, we propose a R-D and complexity joint optimization framework. Within this framework, we develop a simple method that determines for each MB which partitions are likely to be optimal. MV search is carried out for only the selected partitions, thus reducing the complexity of the ME step. The mode selection criteria is based on a measure of spatiotemporal activity within the MB. The procedure minimizes the coding loss at a given level of computational complexity either for the full video sequence or for each single frame. For the latter case, the algorithm provides a tight upper bound on the worst case complexity/execution time of the ME module. Simulation results show that the algorithm speeds up integer-pel ME by a factor of up to 40 with less than 0.2 dB loss in coding efficiency.Publisher's Versio