Hypergraph partitioning (HGP) is an NP-hard problem that occurs in many computer science applications where it is necessary to reduce large problems into a number of smaller, computationally tractable subproblems. Cur...
详细信息
Hypergraph partitioning (HGP) is an NP-hard problem that occurs in many computer science applications where it is necessary to reduce large problems into a number of smaller, computationally tractable subproblems. Current techniques use a multilevel approach wherein an initial partitioning is performed after compressing the hypergraph to a predetermined level. This level is typically chosen to produce very coarse hypergraphs in which heuristic algorithms are fast and effective. This paper presents a novel memetic algorithm which remains effective on larger initial hypergraphs. This enables the exploitation of information that can be lost during coarsening and results in improved final solution quality. We use this algorithm to present an empirical analysis of the space of possible initial hypergraphs in terms of its searchability at different levels of coarsening. We find that the best results arise at coarsening levels unique to each hypergraph. Based on this, we introduce an adaptive scheme that stops coarsening when the rate of information loss in a hypergraph becomes nonlinear and show that this produces further improvements. The results show that we have identified a valuable role for evolutionary algorithms within the current state-of-the-art HGP framework.
In this paper, the authors introduce a robust numerical technique for radiation-conduction heat transfer in the high temperature fields of gas turbine combustors. The conduction and radiation effects are analyzed by a...
详细信息
In this paper, the authors introduce a robust numerical technique for radiation-conduction heat transfer in the high temperature fields of gas turbine combustors. The conduction and radiation effects are analyzed by a differential and an integral equation, respectively. Using discrete ordinates for the angular discretization of the integral equation for the radiation effects and a Galerkin discretization for the heat equation, the authors propose a fast multilevel algorithm to solve the fully discretized problem. The algorithm uses the same mesh hierarchy for both radiation and conduction effects, but with two different smoothing operators. Numerical results are shown for test problems in three space dimensions, and comparisons to other methods are also given.
A fast algorithm for compact fixed-point problems with nonsmooth nonlinearities is designed and analyzed. The algorithm is a combination of an extension of the Atkinson-Brakhage-Nystrom algorithm for smooth problems a...
详细信息
A fast algorithm for compact fixed-point problems with nonsmooth nonlinearities is designed and analyzed. The algorithm is a combination of an extension of the Atkinson-Brakhage-Nystrom algorithm for smooth problems and a generalization of work by Yamamoto and Chen for nonsmooth problems. A critical structural hypothesis in the general theory is explicitly verified in the context of problems that can be expressed as integral equations with certain types of nonsmoothness. The work is motivated by problems in combat modeling. In particular, we consider the solution of an optimality system that arises in control of competitive systems.
In orientation to new developments in evolutionary biology we propose an extension of evolutionary algorithms in two dimensions, the regulatory algorithm (RGA). It consists of two levels of vectors, the regulatory vec...
详细信息
In orientation to new developments in evolutionary biology we propose an extension of evolutionary algorithms in two dimensions, the regulatory algorithm (RGA). It consists of two levels of vectors, the regulatory vector and the structural vector. Each element of the regulatory vector is connected with one or several elements of the structural vector, but not vice versa. The connections can be interpreted as steering connections, the switching on or off of the structural elements and/or as switching orders for the structural elements. An RGA that operates with the usual genetic operators of mutation and crossover can be used for avoiding rules like penalty or default operators, it is in certain problems significantly faster than a standard genetic algorithm, and it is very suited when modeling and optimizing systems that consist themselves of different levels. Examples of RGA usage are shown, namely, the optimal dividing of socially deviant youths in a hostel, the optimal introduction of communication standards in information systems, and the allocation of employees to superiors by taking into regard the different personality types.
An algorithm for the fast computation of the physical optics (PO) integral describing single bounce back scattering in near-field scenarios is presented. The algorithm is based on a multilevel computation of partial c...
详细信息
An algorithm for the fast computation of the physical optics (PO) integral describing single bounce back scattering in near-field scenarios is presented. The algorithm is based on a multilevel computation of partial contributions to the PO integral by hierarchically ordered subdomains. Phase- and amplitude-compensation of the partial contributions allows for their coarse sampling over non-uniform spherical grids. The solution is obtained by gradual aggregation of such partial contributions via interpolation on progressively denser grids. The computational complexity is further reduced by representation of small subdomains' contributions via their far-field patterns and transition to the near-field representations only at a higher level. Speed-up, accuracy, and error controllability are demonstrated.
A partially asynchronous co-state prediction algorithm for the solution of the optimal control problem of linear large-scale systems is presented. A detailed study of the convergence behaviour of the proposed algorith...
详细信息
A partially asynchronous co-state prediction algorithm for the solution of the optimal control problem of linear large-scale systems is presented. A detailed study of the convergence behaviour of the proposed algorithm is given, taking into consideration the effect of communication delay among the processors forming the overall system. The results of applying the new algorithm to simulation examples are presented and compared with those obtained using the well-known synchronous algorithm.
We combine the adaptive and multilevel approaches to the BDDC and formulate a method which allows an adaptive selection of constraints on each decomposition level. We also present a strategy for the solution of local ...
详细信息
We combine the adaptive and multilevel approaches to the BDDC and formulate a method which allows an adaptive selection of constraints on each decomposition level. We also present a strategy for the solution of local eigenvalue problems in the adaptive algorithm using the LOBPCG method with a preconditioner based on standard components of the BDDC. The effectiveness of the method is illustrated on several engineering problems. It appears that the Adaptive-multilevel BDDC algorithm is able to effectively detect troublesome parts on each decomposition level and improve convergence of the method. The developed open-source parallel implementation shows a good scalability as well as applicability to very large problems and core counts.
By deploying virtualized network elements (hosts, switches, routers, links, etc.) on clusters of commodity machines, distributed network emulations (DNE) closely mimic the behaviors of network systems and provide real...
详细信息
By deploying virtualized network elements (hosts, switches, routers, links, etc.) on clusters of commodity machines, distributed network emulations (DNE) closely mimic the behaviors of network systems and provide real-time interactions and analysis for network service management. However, DNE encounters scalability challenges when faced with large network topologies. These challenges can be boiled down to the assignment problem: to which physical machine each virtualized network element should be assigned so that the largest possible network topology can be emulated? In this paper, we tackle this problem from an algorithmic perspective. We first propose TBR (topology balancing relaxation) as the relaxation of the assignment problem. TBR tries to maintain a balance of the hardware resource consumption, by minimizing the maximum inter-machine bandwidth. We further develop TBS (topology balancing solver), which combines mathematical techniques with multi-level algorithms to solve TBR efficiently. We integrate TBR and TBS into MaxiNet, a famous distributed network emulator. Experimental results show that with the same available physical resources, TBR and TBS can improve emulation scalability by up to 4.7x compared to baselines.
We study the numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic algorithms and provide matching upper error bounds with the help of...
详细信息
We study the numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic algorithms and provide matching upper error bounds with the help of suitable multilevel algorithms and changing-dimension algorithms. More precisely, the spaces of integrands we consider are weighted, reproducing kernel Hilbert spaces with norms induced by an underlying anchored function space decomposition. Here the weights model the relative importance of different groups of variables. The error criterion used is the deterministic worst-case error. We study two cost models for function evaluations that depend on the number of active variables of the chosen sample points, and we study two classes of weights, namely product and order-dependent weights and the newly introduced finite projective dimension weights. We show for these classes of weights that multilevel algorithms achieve the optimal rate of convergence in the first cost model while changing-dimension algorithms achieve the optimal convergence rate in the second model. As an illustrative example, we discuss the anchored Sobolev space with smoothness parameter and provide new optimal quasi-Monte Carlo multilevel algorithms and quasi-Monte Carlo changing-dimension algorithms based on higher-order polynomial lattice rules.
multilevel partitioning methods that are inspired by principles of multiscaling are the most powerful practical hypergraph partitioning solvers. Hypergraph partitioning has many applications in disciplines ranging fro...
详细信息
multilevel partitioning methods that are inspired by principles of multiscaling are the most powerful practical hypergraph partitioning solvers. Hypergraph partitioning has many applications in disciplines ranging from scientific computing to data science. In this paper we introduce the concept of algebraic distance on hypergraphs and demonstrate its use as an algorithmic component in the coarsening stage of multilevel hypergraph partitioning solvers. The algebraic distance is a vertex distance measure that extends hyperedge weights for capturing the local connectivity of vertices which is critical for hypergraph coarsening schemes. The practical effectiveness of the proposed measure and corresponding coarsening scheme is demonstrated through extensive computational experiments on a diverse set of problems. Finally, we propose a benchmark of hypergraph partitioning problems to compare the quality of other solvers.
暂无评论