Pregel's vertex-centric model allows us to implement many interesting graph algorithms, where optimization plays an important role in making it practically useful. Although many optimizations have been developed for dealing with different performance issues, it is hard to compose them together to optimize complex algorithms, where we have to deal with multiple performance issues at the same time. In this paper, we propose a new approach to composing optimizations, by making use of the interface, as a replacement of Pregel's message passing and aggregator mechanism, which can better structure the communication in Pregel algorithms. We demonstrate that it is convenient to optimize a Pregel program by simply using a proper channel from the channel library or composing them to deal with multiple performance issues. We intensively evaluate the approach through many nontrivial examples. By adopting the channel interface, our system achieves an all-around performance gain for various graph algorithms. In particular, the composition of different optimizations makes the S-V algorithm 2.20x faster than the current best implementation.
There has been much research studying the optimizations on Pregel-like systems, and our optimized channels draw inspiration from this line of research, such as the sender-side message combining (a.k.a. vertex-replication, mirroring) @cite_22 @cite_24 @cite_29 @cite_30 , the request-respond paradigm @cite_13 , the block-centric model @cite_0 @cite_10 @cite_17 and so on. In particular, our scatter-combine channel recognizes the static messaging pattern and reduces the computational cost as well as message size by pre-processing, which is novel and turns out to be effective for com -mu -ni -ca -tion-intensive algorithms like PageRank and S-V. We also demonstrate how complex algorithms like S-V and SCC can be optimized by such technique, while most existing systems only focus on rather simple algorithms.
@cite_30 @cite_22 @cite_10 @cite_29 @cite_24 @cite_0 @cite_13 @cite_17
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In this paper, we propose a joint subchannel and power allocation algorithm for the downlink of an orthogonal frequency-division multiple access (OFDMA) mixed femtocell macrocell network deployment. Specifically, the total throughput of all femtocell user equipments (FUEs) is maximized while the network capacity of an existing macrocell is always protected. Towards this end, we employ an iterative approach in which OFDM subchannels and transmit powers of base stations (BS) are alternatively assigned and optimized at every step. For a fixed power allocation, we prove that the optimal policy in each cell is to give each subchannel to the user with the highest signal-to-interference-plus-noise ratio (SINR) on that subchannel. For a given subchannel assignment, we adopt the successive convex approximation (SCA) approach and transform the highly nonconvex power allocation problem into a sequence of convex subproblems. In the arithmetic-geometric mean (AGM) approximation, we apply geometric programming to find optimal solutions after condensing a posynomial into a monomial. On the other hand, logarithmic and d ifference-of-two- c oncave-functions (D.C.) approximations lead us to solving a series of convex relaxation programs. With the three proposed SCA-based power optimization solutions, we show that the overall joint subchannel and power allocation algorithm converges to some local maximum of the original design problem. While a central processing unit is required to implement the AGM approximation-based solution, each BS locally computes the optimal subchannel and power allocation for its own servicing cell in the logarithmic and D.C. approximation-based solutions. Numerical examples confirm the merits of the proposed algorithm. In this paper we introduce a novel linear precoding technique. The approach used for the design of the precoding matrix is general and the resulting algorithm can address several optimization criteria with an arbitrary number of antennas at the user terminals. We have achieved this by designing the precoding matrices in two steps. In the first step we minimize the overlap of the row spaces spanned by the effective channel matrices of different users using a new cost function. In the next step, we optimize the system performance with respect to specific optimization criteria assuming a set of parallel single- user MIMO channels. By combining the closed form solution with Tomlinson-Harashima precoding we reach the maximum sum-rate capacity when the total number of antennas at the user terminals is less or equal to the number of antennas at the base station. By iterating the closed form solution with appropriate power loading we are able to extract the full diversity in the system and reach the maximum sum-rate capacity in case of high multi-user interference. Joint processing over a group of multi-user MIMO channels in different frequency and time slots yields maximum diversity regardless of the level of multi-user interference. We consider the MIMO broadcast channel (MIMO-BC) where an array equipped with M antennas transmits distinct information to K users, each equipped with N antennas. We propose a linear precoding technique, called multiuser eigenmode transmission (MET), based on the block diagonalization precoding technique. MET addresses the shortcomings of previous ZF-based beamformers by transmitting to each user on one or more eigenmodes chosen using a greedy algorithm. We consider both the typical sum-power constraint (SPC), and a per-antenna power constraint (PAPC) motivated by array architectures where antennas are powered by separate amplifiers and are either co-located or spatially separated. Numerical results show that the proposed MET technique outperforms previous linear techniques with both SPC and PAPC. Asymptotically as the number of user K increases without bound, we show that block diagonalization with receive antenna selection under PAPC and SPC are asymptotically optimal. We present a novel boundary integral formulation of the Helmholtz transmission problem for bounded composite scatterers (that is, piecewise constant material parameters in "subdomains") that directly lends itself to operator preconditioning via Calderon projectors. The method relies on local traces on subdomains and weak enforcement of transmission conditions. The variational formulation is set in Cartesian products of standard Dirichlet and special Neumann trace spaces for which restriction and extension by zero are well defined. In particular, the Neumann trace spaces over each subdomain boundary are built as piecewise @math -distributions over each associated interface. Through the use of interior Calderon projectors, the problem is cast in variational Galerkin form with an operator matrix whose diagonal is composed of block boundary integral operators associated with the subdomains. We show existence and uniqueness of solutions based on an extension of Lions' projection lemma for non-closed subspaces. We also investigate asymptotic quasi-optimality of conforming boundary element Galerkin discretization. Numerical experiments in 2-D confirm the efficacy of the method and a performance matching that of another widely used boundary element discretization. They also demonstrate its amenability to different types of preconditioning.