Factoring Semiprimes Using PG2N Prime Graph Multiagent Search

In this thesis a heuristic method for factoring semiprimes by multiagent depth-limited search of PG2N graphs is presented. An analysis of PG2Nn graph connectivity is used to generate heuristics for multiagent search. Further analysis is presented including the requirements on choosing prime numbers to generate \u27hard\u27 semiprimes; the lack of connectivity in PG1N graphs; the counts of spanning trees in PG2N graphs; the upper bound of a PG2N graph diameter and a conjecture on the frequency distribution of prime numbers on Hamming distance. We further demonstrated the feasibility of the HD2 breadth first search of PG2N graphs for factoring small semiprimes. We presented the performance of different multiagent search heuristics in PG2N graphs showing that the heuristic of most connected seedpick outperforms least connected or random connected seedpick heuristics on small PG2N graphs of size NN

Large-scale analysis of phylogenetic search behavior

Phylogenetic analysis is used in all branches of biology by inferring evolutionary trees. Applications include designing more effective drugs, tracing the transmission of deadly viruses, and guiding conservation and biodiversity efforts. Most analyses rely on effective heuristics for obtaining accurate trees. However, relatively little work has been done to analyze quantitatively the behavior of phylogenetic heuristics in tree space. This is important, because a better understanding of local search behavior can facilitate the design of better heuristics, which ultimately leads to more accurate depictions of the true evolutionary relationships. In order to access and analyze the tree search space, we implement an effec- tive local search heuristic. Having an effective heuristic that can open the space is important, since no search heuristic in this field can effectively provide data collec- tion control. So we have implemented and estimated a search heuristic, Simple Local Search or SLS, that works reasonably well in the space. Our investigations led to several interesting observations about the behavior of a search heuristic and the tree search space. We studied the correlation of tree features of search path trees, where tree features refer to the parsimony score, the Robinson- Foulds distance and the homoplasy measure. Most importantly from the results, parsimony score was highly correlated with Robinson-Foulds distance only in trees that lie on the search path to a local optimum. We also note that the scores of neighborhoods along search paths improve together, as a local search progresses. Correlations of tree features of search path trees are particularly useful in char- acterizing and controlling a search path. This paper proposes one possible stopping criterion to maximize the tree search results while minimizing computational time tested on three biological datasets using the correlation between the parsimony score and the RF distance value of search path trees. Also, the observation that scores of a neighborhood on a search path improve together gives us a significant amount of flexibility in selecting the next pivot of a search without losing performance. Eventually, our long-term goal is developing an effective search heuristic that can deal with large scale tree space in reasonable time. Improved knowledge about the tree search space and the search heuristic can provide a reasonable starting point toward the goal

Metaheuristic approaches for the quartet method of hierarchical clustering

Given a set of objects and their pairwise distances, we wish to determine a visual representation of the data. We use the quartet paradigm to compute a hierarchy of clusters of the objects. The method is based on an NP-hard graph optimization problem called the Minimum Quartet Tree Cost problem. This paper presents and compares several metaheuristic approaches to approximate the optimal hierarchy. The performance of the algorithms is tested through extensive computational experiments and it is shown that the Reduced Variable Neighbourhood Search metaheuristic is the most effective approach to the problem, obtaining high quality solutions in short computational running times

On Optimizing Distributed Tucker Decomposition for Dense Tensors

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component analysis (PCA)and finds applications in diverse domains such as signal processing, computer vision and text analytics. Our objective is to develop an efficient distributed implementation for the case of dense tensors. The implementation is based on the HOOI (Higher Order Orthogonal Iterator) procedure, wherein the tensor-times-matrix product forms the core routine. Prior work have proposed heuristics for reducing the computational load and communication volume incurred by the routine. We study the two metrics in a formal and systematic manner, and design strategies that are optimal under the two fundamental metrics. Our experimental evaluation on a large benchmark of tensors shows that the optimal strategies provide significant reduction in load and volume compared to prior heuristics, and provide up to 7x speed-up in the overall running time.Comment: Preliminary version of the paper appears in the proceedings of IPDPS'1

Improved Memory-Bounded Dynamic Programming for Decentralized POMDPs

Memory-Bounded Dynamic Programming (MBDP) has proved extremely effective in solving decentralized POMDPs with large horizons. We generalize the algorithm and improve its scalability by reducing the complexity with respect to the number of observations from exponential to polynomial. We derive error bounds on solution quality with respect to this new approximation and analyze the convergence behavior. To evaluate the effectiveness of the improvements, we introduce a new, larger benchmark problem. Experimental results show that despite the high complexity of decentralized POMDPs, scalable solution techniques such as MBDP perform surprisingly well.Comment: Appears in Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence (UAI2007

Low Cost Quality of Service Multicast Routing in High Speed Networks

Many of the services envisaged for high speed networks, such as B-ISDN/ATM, will support real-time applications with large numbers of users. Examples of these types of application range from those used by closed groups, such as private video meetings or conferences, where all participants must be known to the sender, to applications used by open groups, such as video lectures, where partcipants need not be known by the sender. These types of application will require high volumes of network resources in addition to the real-time delay constraints on data delivery. For these reasons, several multicast routing heuristics have been proposed to support both interactive and distribution multimedia services, in high speed networks. The objective of such heuristics is to minimise the multicast tree cost while maintaining a real-time bound on delay. Previous evaluation work has compared the relative average performance of some of these heuristics and concludes that they are generally efficient, although some perform better for small multicast groups and others perform better for larger groups. Firstly, we present a detailed analysis and evaluation of some of these heuristics which illustrates that in some situations their average performance is reversed; a heuristic that in general produces efficient solutions for small multicasts may sometimes produce a more efficient solution for a particular large multicast, in a specific network. Also, in a limited number of cases using Dijkstra's algorithm produces the best result. We conclude that the efficiency of a heuristic solution depends on the topology of both the network and the multicast, and that it is difficult to predict. Because of this unpredictability we propose the integration of two heuristics with Dijkstra's shortest path tree algorithm to produce a hybrid that consistently generates efficient multicast solutions for all possible multicast groups in any network. These heuristics are based on Dijkstra's algorithm which maintains acceptable time complexity for the hybrid, and they rarely produce inefficient solutions for the same network/multicast. The resulting performance attained is generally good and in the rare worst cases is that of the shortest path tree. The performance of our hybrid is supported by our evaluation results. Secondly, we examine the stability of multicast trees where multicast group membership is dynamic. We conclude that, in general, the more efficient the solution of a heuristic is, the less stable the multicast tree will be as multicast group membership changes. For this reason, while the hybrid solution we propose might be suitable for use with closed user group multicasts, which are likely to be stable, we need a different approach for open user group multicasting, where group membership may be highly volatile. We propose an extension to an existing heuristic that ensures multicast tree stability where multicast group membership is dynamic. Although this extension decreases the efficiency of the heuristics solutions, its performance is significantly better than that of the worst case, a shortest path tree. Finally, we consider how we might apply the hybrid and the extended heuristic in current and future multicast routing protocols for the Internet and for ATM Networks.