This paper proposes a fast safe-region generation method for several kinds of vicinity queries including set k nearest neighbor (NN) queries, ordered kNN queries, reverse kNN queries, and distance range queries. When a user is driving a car on a road network, he/she wants to know about objects located in the vicinity of the car. However, the result changes according to the movement of the car, and therefore, the user needs to request up-to-date result to the server. On the other hand, frequent requests for up-to-date results cause heavy loadings on the server. To cope with this problem efficiently, the idea of the safe-region has been proposed, however, it takes long processing time in existing works. This paper proposes a fast generation method of the safe-region applicable to several types of vicinity queries. Through experimental evaluations, we demonstrate that the proposed method outperforms the existing algorithms in the processing time by one or two orders of magnitude.

The increasing demand for high-performance computing in recent years has led to active research on massively parallel systems. The interconnection network in a massively parallel system interconnects hundreds of thousands of processing elements so that they can process large tasks while communicating among others. By regarding the processing elements as nodes and the links between processing elements as edges, respectively, we can discuss various problems of interconnection networks in the framework of the graph theory. Many topologies have been proposed for interconnection networks of massively parallel systems. The hypercube is a very popular topology and it has many variants. The cross-cube is such a topology, which can be obtained by adding one extra edge to each node of the hypercube. The cross-cube reduces the diameter of the hypercube, and allows cycles of odd lengths. Therefore, we focus on the cross-cube and propose an algorithm that constructs disjoint paths from a node to a set of nodes. We give a proof of correctness of the algorithm. Also, we show that the time complexity and the maximum path length of the algorithm are O(n3 log n) and 2n - 3, respectively. Moreover, we estimate that the average execution time of the algorithm is O(n2) based on a computer experiment.

Searching for the shortest paths from a query point to several target points on a road network is an essential operation for several types of queries in location-based services. This search can be performed using Dijkstra's algorithm. Although the A* algorithm is faster than Dijkstra's algorithm for finding the shortest path from a query point to a target point, the A* algorithm is not so fast to find all paths between each point and the query point when several target points are given. In this case, the search areas on road network overlap for each search, and the total number of operations at each node is increased, especially when the number of query points increases. In the present paper, we propose the single-source multi-target A* (SSMTA*) algorithm, which is a multi-target version of the A* algorithm. The SSMTA* algorithm guarantees at most one operation for each road network node, and the searched area on road network is smaller than that of Dijkstra's algorithm. Deng et al. proposed the LBC approach with the same objective. However, several heaps are used to manage the search area on the road network and the contents in each heap must always be kept the same in their method. This operation requires much processing time. Since the proposed method uses only one heap, such content synchronization is not necessary. The present paper demonstrates through empirical evaluations that the proposed method outperforms other similar methods.

In this paper, we propose two algorithms, B-N2N and B-N2S, that solve the node-to-node and node-to-set disjoint paths problems in the bicube, respectively. We prove their correctness and that the time complexities of the B-N2N and B-N2S algorithms are O(n2) and O(n2 log n), respectively, if they are applied in an n-dimensional bicube with n ≥ 5. Also, we prove that the maximum lengths of the paths generated by B-N2N and B-N2S are both n + 2. Furthermore, we have shown that the algorithms can be applied in the locally twisted cube, too, with the same performance.

The bicube is derived from the hypercube, and it provides a topology for interconnection networks of parallel systems. The bicube can interconnect the same number of nodes with the same degree as the hypercube while its diameter is almost half of that of the hypercube. In addition, the bicube preserves the property of node symmetry. Hence, the bicube attracts much attention. In this paper, we focus on the bicube with faulty nodes and propose three fault-tolerant routing methods to find a fault-free path between any pair of non-faulty nodes in it.