On the weak k -metric dimension of Hamming graphs

In this paper, we propose a model-based approach to parallelize Simulink models on multicore CPUs and NVIDIA GPUs at the block level and generate CUDA C codes for parallel execution. In our proposed approach, the Simulink models are converted to directed acyclic graphs (DAGs) based on their block diagrams, wherein the nodes represent tasks of grouped blocks in the model and the edges represent the communication behaviors between blocks. Next, a path analysis is conducted on the DAGs to extract all execution paths and calculate the length of each path, which comprises the execution times of tasks and the communication times of edges on the path. Then, an integer linear programming (ILP) formulation is used to minimize the length of the critical path of the DAG, which represents the execution time of the Simulink model. The ILP formulation also balances the workloads on each CPU core for optimized hardware utilization. We evaluate the proposed approach by parallelizing an image processing model on a platform of two homogeneous CPU cores and two GPUs to determine its effectiveness.

In this paper we propose a model-based approach to parallelize Simulink models of image processing algorithms on homogeneous multicore CPUs and NVIDIA GPUs at the block level and generate CUDA C codes for parallel execution on the target hardware. In the proposed approach, the Simulink models are converted to directed acyclic graphs (DAGs) based on their block diagrams, wherein the nodes represent tasks of grouped blocks or subsystems in the model and the edges represent the communication behaviors between blocks. Next, a path analysis is conducted on the DAGs to extract all execution paths and calculate their respective lengths, which comprises the execution times of tasks and the communication times of edges on the path. Then, an integer linear programming (ILP) formulation is used to minimize the length of the critical path of the DAG, which represents the execution time of the Simulink model. The ILP formulation also balances workloads on each CPU core for optimized hardware utilization. We parallelized image processing models on a platform of two homogeneous CPU cores and two GPUs with our approach and observed a speedup performance between 8.78x and 15.71x.

The solution of the shortest path problem in case of time-independent edge-lengths is due to FORD and FULKERSON [1,2]. By using the method of dynamic programming, BELLMAN [3] gave a procedure for the determination of the length of the shortest path. Following this principle COOKE and HALSEY [4] have a procedure for the determination of the length of the shortest path in case of time-dependent edge-lengths. This procedure, however, gives only the length of the path, not the path itself. We shall demonstrate in this paper that the method of FORD and FULKERSON leads itself too to solution of the problem, morcover it gives also the shortest path.

In plants and other multicellular organisms, cells work together in tissues and organs to achieve outcomes that they would not be able to accomplish on their own. For example, the cells that make up the stem of a plant hold the leaves, flowers and other organs in place, and provide a transport network that allows molecules to move around the plant. Mapping the locations of cells within tissues and analysing the connections between them will help researchers to understand how the organisation of tissues influences the tasks cells perform. There are several different layers of tissue within a plant’s stem. The surface of the stem has a protective layer of tissue called epidermis. The epidermis contains two different types of cells known as trichoblasts and atrichoblasts, but it was not clear why these cells are organised the way they are. Arabidopsis thaliana is a small plant that is often used in studies of how plants grow and develop. Jackson et al. combined microscopy with computational techniques to study the stems of young A. thaliana seedlings. The experiments reveal that the two types of epidermal cells appear to adopt distinct roles. The trichoblasts form hair-like structures and acquire nutrients from the external environment, while their neighbours the atrichoblasts provide shortcut routes for these nutrients to be unloaded and moved up the stem. This pattern was not present in several other plant species including foxglove or poppy, suggesting it may be an adaptation in A. thaliana plants that helps them grow in the particular environments this plant faces. The findings of Jackson et al. show that cells are carefully arranged in plant stems and suggest that there is an optimal way for a plant to make a stem depending on its environment. Further work is now needed to understand how different molecules use the shortcuts provided by the atrichoblasts during plant development, and whether alternative configurations are possible. In the future, such studies may help provide a framework to genetically engineer plants that are better adapted to grow in different environments.

The classical Duplication-Loss-Coalescence parsimony model (DLC-model) is a powerful tool when studying the complex evolutionary scenarios of simultaneous duplication-loss and deep coalescence events in evolutionary histories of gene families. However, inferring such scenarios is an intrinsically difficult problem and, therefore, prohibitive for larger gene families typically occurring in practice. To overcome this stringent limitation, we make the first step by describing a non-trivial and flexible Integer Linear Programming (ILP) formulation for inferring DLC evolutionary scenarios. To make the DLC-model more practical, we then introduce two sensibly constrained versions of the model and describe two respectively modified versions of our ILP formulation reflecting these constraints. Using a simulation study, we showcase that our constrained ILP formulation computes evolutionary scenarios that are substantially larger than the scenarios computable under our original ILP formulation and DLCPar. Further, scenarios computed under our constrained DLC-model are overall remarkably accurate when compared to corresponding scenarios under the original DLC-model.

This paper investigates the problem of optimal diverse routing for shared path-based protection in the complete routing information scenario on mesh optical networks, where a novel Integer Linear Programming (ILP) formulation is introduced such that the least-cost link-disjoint working and protection path-pair can be derived in a single step. The proposed ILP formulation is characterized by the facts that it is solvable with the commercially available Linear Programming (LP) solvers and that it can deal with the dependency between working and spare capacity in the network, which is a step ahead of the most state-of-the-art techniques in the design of diverse routing algorithms for shared protection. To verify the proposed ILP, an experiment is conducted to compare it with four reported schemes for end-to-end shared protection on two network topologies, namely APFPBC, MLR, ITSA, and ILP-2S, where blocking probability is taken as the performance metric with connection requests being dynamically launched into the networks. The simulation results show that the ILP formulation yields the best performance while the ILP-2S scheme investigating less network states yields the worst. We also use the results by the proposed ILP to evaluate the four heuristic-based schemes adopted in the simulation in terms of two performance indexes – the percentage of optimality (denoted as %opti) and the offset of optimality (denoted as Q).

Traffic grooming techniques are used to combine low-speed data streams onto high-speed lightpaths with the objective of minimizing the network cost, or maximizing the network throughput. In this paper, we first present an efficient integer linear program (ILP) formulation for traffic grooming on mesh WDM networks. Our formulation can be easily modified to implement different objective functions. Unlike previous formulations, our ILP formulation can be used for practical sized networks with several hundred requests. We then propose a second ILP for traffic grooming, with the simplifying assumption that RWA is not an issue. This second formulation is able to generate, in a reasonable time, grooming strategies, for networks with over 30 nodes, with hundreds and even thousands of low-speed data streams. Finally, we introduce a set of ILP formulations for traffic grooming, where the logical topology is specified. We have studied, using simulation, the time needed to determine grooming strategies, using the different ILP formulations.

The classical Duplication-Loss-Coalescence parsimony model (DLC-model) is a powerful tool when studying the complex evolutionary scenarios of simultaneous duplication-loss and deep coalescence events in evolutionary histories of gene families. However, inferring such scenarios is an intrinsically difficult problem and, therefore, prohibitive for larger gene families typically occurring in practice. The parsimony duplication-loss-coalescence model (DLCParsimony model) appeared as an effective way to study commonly appearing gene families, whose evolutionary histories had duplication-loss events appearing alongside the incomplete lineage sorting events. This model allows practitioners to accurately infer ortholog/paralog relationships among extant genes and to study the relationship between the gene family evolution (gene tree) and the host species evolution (species tree). Unfortunately, the existing enumeration algorithm, DLCPar, which finds the optimum reconciliation between a gene tree and a species tree under the DLCParsimony model, is very limited in practice due to its advanced complexity. To overcome this stringent limitation, we first describe a non-trivial and flexible Integer Linear Programming (ILP) formulation for inferring DLC evolutionary scenarios. A comparative scalability study demonstrates that our ILP formulation commonly outperforms the standard enumeration algorithm DLCPar for inferring scenarios under the DLC-model. To make the DLC-model more practical, we then introduce two sensibly constrained versions of the model and describe two respectively modified versions of our ILP formulation reflecting these constraints. Using a simulation study, we showcase that our constrained ILP formulation computes evolutionary scenarios that are substantially larger than the scenarios computable under our original ILP formulation and DLCPar. Further, scenarios computed under our constrained DLC-model are overall remarkably accurate when compared to corresponding scenarios under the original DLC-model.

In this paper, we address the constrained two‐dimensional rectangular guillotine single large placement problem (2D_R_CG_SLOPP). This problem involves cutting a rectangular object to produce smaller rectangular items from orthogonal guillotine cuts. In addition, there is an upper limit on the number of copies that can be produced of each item type. To model this problem, we propose a new pseudopolynomial integer nonlinear programming (INLP) formulation and obtain an equivalent integer linear programming (ILP) formulation from it. Additionally, we developed a procedure to reduce the numbers of variables and constraints of the integer linear programming (ILP) formulation, without loss of optimality. From the ILP formulation, we derive two new pseudopolynomial models for particular cases of the 2D_R_CG_SLOPP, which consider only two‐staged or one‐group patterns. Finally, as a specific solution method for the 2D_R_CG_SLOPP, we apply Benders decomposition to the proposed ILP formulation and develop a branch‐and‐Benders‐cut algorithm. All proposed approaches are evaluated through computational experiments using benchmark instances and compared with other formulations available in the literature. The results show that the new formulations are appropriate in scenarios characterized by few item types that are large with respect to the object's dimensions.

In this paper heuristics are proposed for finding the shortest loopless path, from a source node to a target node, that visits a given set of nodes in a directed graph, such that it can be protected using a node-disjoint path. This type of problem may arise due to network management constraints.The problem of calculating the shortest path that visits a given set of nodes is at least as difficult as the traveling salesman problem, and it has not received much attention. Nevertheless an efficient integer linear programming (ILP) formulation has been recently proposed for this problem. Here, the ILP formulation is adapted to include the constraint that the obtained path will be able to be protected by a node-disjoint path. Computational experiments show that this approach, namely in large networks, may fail to obtain a solution in a reasonable amount of time. Therefore three versions of a heuristic are proposed, for which extensive computational results show that they are able to find a solution in most cases, and that the calculated solutions present an acceptable relative error regarding the cost of the optimal active path. Further the CPU time required by the heuristics is significantly smaller than the required by the used ILP solver.

The duplication-loss-coalescence (DLC) parsimony model is invaluable for analyzing the complex scenarios of concurrent duplication loss and deep coalescence events in the evolution of gene families. However, inferring such scenarios for already moderately sized families is prohibitive owing to the computational complexity involved. To overcome this stringent limitation, we make the first step by describing a flexible integer linear programming (ILP) formulation for inferring DLC evolutionary scenarios. Then, to make the DLC model more scalable, we introduce four sensibly constrained versions of the model and describe modified versions of our ILP formulation reflecting these constraints. Our simulation studies showcase that our constrained ILP formulations compute evolutionary scenarios that are substantially larger than scenarios computable under our original ILP formulation and the original dynamic programming algorithm by Wu et al. Furthermore, scenarios computed under our constrained DLC models are remarkably accurate compared with corresponding scenarios under the original DLC model, which we also confirm in an empirical study with thousands of gene families.

This paper describes the theory and algorithms of fuzzy distance transform (FDT). Fuzzy distance is defined as the length of the shortest path between two points. The length of a path in a fuzzy subset is defined as the integration of fuzzy membership values of the points along the path. The shortest path between two points is the one with the minimum length among all (infinitely many) paths between the two points. It is demonstrated that, unlike in the binary case, the shortest path in a fuzzy subset is not necessarily a straight-line segment. The support of a fuzzy subset is the set of points with nonzero membership values. It is shown that, for any fuzzy subset, fuzzy distance is a metric for the interior of its support. FDT is defined as the process on a fuzzy subset that assigns at each point the smallest fuzzy distance from the boundary of the support. The theoretical framework of FDT in continuous space is extended to digital spaces and a dynamic programming-based algorithm is presented for its computation. Several potential medical imaging applications are presented including the quantification of blood vessels and trabecular bone thickness in the regime of limited special resolution.

There has been considerable research interest in the design of survivable grooming capable networks in recent years. For such networks, protection may take place at the lightpath level or at the connection level. The vast majority of the current work can be classified into one of two categories (i) static grooming, where the demands are allocated for the entire duration of the network and (ii) dynamic grooming, where the start times and durations of demands are generated randomly based on certain traffic distributions. In this paper, we propose a new technique for survivable traffic grooming under the scheduled traffic model that exploits knowledge of the connection holding times of traffic demands to lead to more efficient resource allocation. We present efficient integer linear program (ILP) formulations for the complete survivable traffic grooming problem in WDM networks. Our formulations can solve the joint problem of the topology design, traffic routing and RWA, using path protection at lightpath level. Our aim is to design a stable logical topology that can accommodate a collection of low-speed traffic demands with specified setup and teardown times. The objective function, considered in our ILP formulation, is to minimize the resource requirements. This can be easily modified to maximize the throughput under a given set of resources. We also have proposed a simplified version of our ILP formulations that can solve the problem in a way that is computationally more efficient. To the best of our knowledge, this is the first paper to address the survivable traffic grooming problem under the scheduled traffic model.

Consider a weighted graph G whose vertices are points in the plane and edges are line segments between pairs of points whose weight is the Euclidean distance between its endpoints. A routing algorithm on G sends a message from any vertex s to any vertex t in G. The algorithm has a competitive ratio of c if the length of the path taken by the message is at most c times the length of the shortest path from s to t in G. It has a routing ratio of c if the length of the path is at most c times the Euclidean distance from s to t. The algorithm is online if it makes forwarding decisions based on (1) the k-neighborhood in G of the message’s current position (for constant k > 0) and (2) limited information stored in the message header.

The goal of this paper is to design a simplex algorithm for linear programs on lattice polytopes that traces “short” simplex paths from any given vertex to an optimal one. We consider a lattice polytope P contained in $$[0,k]^n$$ and defined via m linear inequalities. Our first contribution is a simplex algorithm that reaches an optimal vertex by tracing a path along the edges of P of length in $$O(n^{4} k\, \hbox {log}\, k).$$ The length of this path is independent from m and it is the best possible up to a polynomial function. In fact, it is only polynomially far from the worst-case diameter, which roughly grows as nk. Motivated by the fact that most known lattice polytopes are defined via $$0,\pm 1$$ constraint matrices, our second contribution is a more sophisticated simplex algorithm which exploits the largest absolute value $$\alpha $$ of the entries in the constraint matrix. We show that the length of the simplex path generated by this algorithm is in $$O(n^2k\, \hbox {log}\, ({nk} \alpha ))$$ . In particular, if $$\alpha $$ is bounded by a polynomial in n, k, then the length of the simplex path is in $$O(n^2k\, \hbox {log}\, (nk))$$ . For both algorithms, if P is “well described”, then the number of arithmetic operations needed to compute the next vertex in the path is polynomial in n, m, and $$\hbox {log}\, k$$ . If k is polynomially bounded in n and m, the algorithm runs in strongly polynomial time.