Search Graph Magnification in Rapid Mixing of Markov Chains Associated with the Local Search-Based Metaheuristics

The structural property of the search graph plays an important role in the success of local search-based metaheuristic algorithms. Magnification is one of the structural properties of the search graph. This study builds the relationship between the magnification of a search graph and the mixing time of Markov Chain (MC) induced by the local search-based metaheuristics on that search space. The result shows that the ergodic reversible Markov chain induced by the local search-based metaheuristics is inversely proportional to magnification. This result indicates that it is desirable to use a search space with large magnification for the optimization problem in hand rather than using any search spaces. The performance of local search-based metaheuristics may be good on such search spaces since the mixing time of the underlying Markov chain is inversely proportional to the magnification of search space. Using these relations, this work shows that MC induced by the Metropolis Algorithm (MA) mixes rapidly if the search graph has a large magnification. This indicates that for any combinatorial optimization problem, the Markov chains associated with the MA mix rapidly i.e., in polynomial time if the underlying search graph has large magnification. The usefulness of the obtained results is illustrated using the 0/1-Knapsack Problem, which is a well-studied combinatorial optimization problem in the literature and is NP-Complete. Using the theoretical results obtained, this work shows that Markov Chains (MCs) associated with the local search-based metaheuristics like random walk and MA for 0/1-Knapsack Problem mixes rapidly.

Learning-Based Efficient Graph Similarity Computation via Multi-Scale Convolutional Set Matching

Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs is typically NP-hard, a series of approximate methods have been proposed with a trade-off between accuracy and speed. Recently, several data-driven approaches based on neural networks have been proposed, most of which model the graph-graph similarity as the inner product of their graph-level representations, with different techniques proposed for generating one embedding per graph. However, using one fixed-dimensional embedding per graph may fail to fully capture graphs in varying sizes and link structures—a limitation that is especially problematic for the task of graph similarity computation, where the goal is to find the fine-grained difference between two graphs. In this paper, we address the problem of graph similarity computation from another perspective, by directly matching two sets of node embeddings without the need to use fixed-dimensional vectors to represent whole graphs for their similarity computation. The model, Graph-Sim, achieves the state-of-the-art performance on four real-world graph datasets under six out of eight settings (here we count a specific dataset and metric combination as one setting), compared to existing popular methods for approximate Graph Edit Distance (GED) and Maximum Common Subgraph (MCS) computation.

Keyword Search over Distributed Graphs with Compressed Signature

Catchphrase search graph has attracted tons research interest, due to the fact the version diagram can speak pleasant for maximum prepared and dependent database and scan the slogan can launch good sized statistics to the customer with out simple data about the sample and language questions. Practically speaking, information photographs may be very huge, for instance, Web-scale diagram containing billions of vertices. The fine in elegance technique utilizing delivered collectively for the calculation of the slogan seek process diagram, after which they do now not deserve to chart a totally huge, because of confined computing power and further area at the server focused. To remedy this hassle, we look at the slogan test graph scale web page is introduced in splendid situation. We first offer calculation effortlessly believe the response request productive questions. In any case, the calculation of flood searching harmless make use of search techniques that obtain huge time and system overhead. To treatment this weak point, we're at that time advise pursuing calculation based totally marks. In precise, we construct that encodes vertex signatures short way an excellent manner from factor to some random catchphrase in the graph. Thus, we can locate solutions to questions by investigating the dearth of way, with the aim that point and correspondence low value. In addition, we changed the diagram facts in the organization after dividing irregular underlying with the goal that the method is primarily based at the sign greater interesting. Finally, the results of our trial show achievability of our proposed method in carrying out watchword top view diagram statistics Web scale.

Modified Ant Algorithm VLSI Planning on the Basis of the Composite Model of the Solution Space

In this paper, the crystal plan is formed by the recursive use of a "guillotine cut". To set the plan means to set the structure of the binary tree of the cuts, i.e. sequence of binary cuts; for internal tree vertices, to indicate the type of the cut H or V; to number the leaves of the tree and indicate the orientation of the modules. The structure of the binary tree of the cuts can be set using the Polish expression on the base of the alphabet A = {M, TR}, where the set of letters M = {mi|i = 1, 2, ..., nМ} corresponds to the leaves of the section tree (regions), and the set R = {H, V} corresponds to the cuts. We propose a way and methods for solving the problems of planning VLSI based on a modified ant colony. The task of synthesizing the section tree of the plan with the choice of types of sections, identification and orientation of the modules in the work is reduced to the task of forming a modified Polish expression with the identification of elements on the composite model of the solution space, including many alternative vertices. To keep the collective evolutionary memory during the life of the ant population and to form the solution of the problem, we use the complete graph G = (X, U) with alternative vertex states. Each vertex may be in one of two alternative states, i.e., α or β, corresponding to the orientation of the module or the type of the cut. The task of synthesizing the Polish expression is formulated as the task of finding the least-cost route on the solution search graph G = (X, U). A distinctive feature is that when building a route, simultaneously with the choice of the vertex xi∈ X, the state of this vertex is selected. The time complexity of the algorithm is O(n2). Experiments have shown that for large dimensions, the time indicators of the developed algorithm exceed those of the compared algorithms with the best values of the objective function.

Computational design of syntheses leading to compound libraries or isotopically labelled targets

Network-search routines over large graphs of retrosynthetic scenarios are adapted to multi-target design operating on one common search graph enabling design of syntheses of compound libraries or isotopically labelled targets.

Laser simulator

A novel technique called laser simulator approach for visibility search graph-based path planning has been developed in this article to determine the optimum collision-free path in unknown environment. With such approach, it is possible to apply constraints on the mobile robot trajectory while navigating in complex terrains such as in factories and road environments, as the first work of its kind. The main advantage of this approach is the ability to be used for both global/local path planning in the presence of constraints and obstacles in unknown environments. The principle of the laser simulator approach with all possibilities and cases that could emerge during path planning is explained to determine the path from initial to destination positions in a two-dimensional map. In addition, a comparative study on the laser simulator approach, A* algorithm, Voronoi diagram with fast marching and PointBug algorithms was performed to show the benefits and drawbacks of the proposed approach. A case study on the utilization of the laser simulator in both global and local path planning has been applied in a road roundabout setting which is regarded as a complex environment for robot path planning. In global path planning, the path is generated within a grid map of the roundabout environment to select the path according to the respective road rules. It is also used to recognize the real roundabout from a sequence of images during local path planning in the real-world system. Results show that the performance of the proposed laser simulator approach in both global and local environments is achieved with low computational and path costs, in which the optimum path from the selected start position to the goal point is tracked accordingly in the presence of the obstacles.

Find the errors, get the better: Enhancing machine translation via word confidence estimation

This paper presents two novel ideas of improving the Machine Translation (MT) quality by applying the word-level quality prediction for the second pass of decoding. In this manner, the word scores estimated by word confidence estimation systems help to reconsider the MT hypotheses for selecting a better candidate rather than accepting the current sub-optimal one. In the first attempt, the selection scope is limited to the MTN-best list, in which our proposed re-ranking features are combined with those of the decoder for re-scoring. Then, the search space is enlarged over the entire search graph, storing many more hypotheses generated during the first pass of decoding. Over all paths containing words of theN-best list, we propose an algorithm to strengthen or weaken them depending on the estimated word quality. In both methods, the highest score candidate after the search becomes the official translation. The results obtained show that both approaches advance the MT quality over the one-pass baseline, and the search graph re-decoding achieves more gains (in BLEU score) thanN-best List Re-ranking method.