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The query processing in a mobile computing environment involves join processing among different sites which include static servers and mobile computers. Because of the presence of asymmetric features in a mobile computing environment, the conventional query processing for a distributed database cannot be directly applied to a mobile computing system. In this paper, we first explore some unique features of a mobile environment and then, in light of these features, devise query processing methods for both join and query processing. Remote mobile joins are said to be effectual if they are, when being interleaved into a join sequence, able to reduce the amount of data transmission cost required for distributed mobile query processing. Since mobile relations are employed as reducers in our proposed query processing cost model, more mobile joins in the query processing lead to less data transmitted through the network. With proper scheduling, interleaving effectual remote mobile joins into a query scheduling can significantly reduce the total amount of data transmission among different sites. A simulator is developed to evaluate the performance of algorithms devised. Our results show that the approach of interleaving the processing of distributed mobile queries with effectual remote mobile joins is not only efficient, but also effective in reducing the total amount of data transmission cost required to process distributed mobile queries.

A multiorder routing strategy is developed which is loop-free even in the presence of link/node failures. Unlike most conventional methods in which the same routing strategy is applied indiscriminately to all nodes in the network, nodes under this proposal may adopt different routing strategies according to the network structure. Formulas are developed to determine the minimal order of routing strategy for each node to eliminate looping completely. A systematic procedure for striking a compromise between the operational overhead and network adaptability is proposed. Several illustrative examples are presented. >

A distributed computing system and cooperating tasks can be represented by a processor graph G/sub p/=(V/sub p/, E/sub p/) and a task graph G/sub T/=(V/sub T/, E/sub T/), respectively. An edge between a pair of nodes in G/sub T/ represents the existence of direct communications between the two corresponding tasks. The maximal number of hops between two processors in G/sub p/ to which two adjacent tasks in G/sub T/ are assigned is called dilation of that assignment. Characterization and use of the number of acceptable assignments for given G/sub T/ and G/sub P/ are treated. Assignments with the dilation less than or equal to one are considered. This dilation constraint represents a special case in which two adjacent tasks in G/sub T/ must be assigned to either a single processor or two adjacent processors in G/sub p/. For the case where N(G/sub T/, G/sub P/) denotes the numbers of acceptable assignments under this constraint, N(G/sub T/, G/sub P/) are derived for arbitrary G/sub T/ and G/sub P/, and a recursive expression is formulated for N(G/sub T/, G/sub P/) when G/sub T/ is a tree. For some restricted cases, either closed-form or recursive-form expressions of N(G/sub T/, G/sub P/) are derived. The results on N(G/sub T/, G/sub P/) are extended to the completely general case, assignments with dilations greater than one, where two adjacent tasks in G/sub T/ can be assigned to any two processors in G/sub P/ which are not necessarily adjacent to each other. >

Two important issues in managing processors in a hypercube are addressed: subcube allocation and task migration to eliminate the system fragmentation caused by allocation and deallocation of subcubes. It is proven that the subcube allocation strategy using a binary reflected Gray code (BRGC), called the GC strategy, possesses the best subcube recognition ability among all strategies using sequential searches. A binary code (BC) is defined as the binary representation of a nonnegative integer, and an extended binary code (EBC) is obtained by permutating the bits of a BC. Similarly, an extended Gray code (EGC) is obtained from a BRGC. The subcube recognition ability of an allocation strategy using multiple EBCs is analyzed and compared to that using multiple EGCs. >

A family of six-regular graphs, called hexagonal meshes or H-meshes, is considered as a multiprocessor interconnection network. Processing nodes on the periphery of an H-mesh are first wrapped around to achieve regularity and homogeneity. The diameter of a wrapped H-mesh is shown to be of O(p/sup 1/2/), where p is the number of nodes in the H-mesh. An elegant, distributed routing scheme is developed for wrapped H-meshes so that each node in an H-mesh can compute shortest paths from itself to any other node with a straightforward algorithm of O(1) using the addresses of the source-destination pair only, i.e. independent of the network's size. This is in sharp contrast with those previously known algorithms that rely on using routing tables. Furthermore, the authors also develop an efficient point-to-point broadcasting algorithm for the H-meshes which is proved to be optimal in the number of required communication steps. The wrapped H-meshes are compared against some other existing multiprocessor interconnection networks, such as hypercubes, trees, and square meshes. The comparison reinforces the attractiveness of the H-mesh architecture. >

A connected hypercube with faulty links and/or nodes is called an injured hypercube. A distributed adaptive fault-tolerant routing scheme is proposed for an injured hypercube in which each node is required to know only the condition of its own links. Despite its simplicity, this scheme is shown to be capable of routing messages successfully in an injured n-dimensional hypercube as long as the number of faulty components is less than n. Moreover, it is proved that this scheme routes messages via shortest paths with a rather high probability, and the expected length of a resulting path is very close so that of a shortest path. Since the assumption that the number of faulty components is less than n in an n-dimensional hypercube might limit the usefulness of the above scheme, a routing scheme based on depth-first search which works in the presence of an arbitrary number of faulty components is introduced. Due to the insufficient information on faulty components, however, the paths chosen by this scheme may not always be the shortest. To guarantee all messages to be routed via shortest paths, the authors propose to equip every node with more information than that on its own links. The effects of this additional information on routing efficiency are analyzed, and the additional information to be kept at each node for the shortest path routing is determined. Several examples and remarks are given to illustrate the results. >

This paper deals with a distributed adaptive routing strategy which is very simple and effective, and is free of a ping-pong-type looping in the presence of network failures. Using the number of time intervals required for a node to recover from a network failure as the measure of network's adaptability, performance of this strategy and the ARPANET's previous routing strategy (APRS) is comparatively analyzed without resorting to simulation. Formulas of the exact number of time intervals required for failure recovery under both strategies are also derived. We show that i)the performance of the strategy is always better than, or at least as good as, that of APRS, and ii) network topology has significant effects on the performance of both strategies.

The processor allocation problem in an n-dimensional hypercube (or an n-cube) multiprocessor is similar to the conventional memory allocation problem. The main objective in both problems is to maximize the utilization of available resources as well as minimize the inherent system fragmentation. A processor allocation strategy using the buddy system, called the buddy strategy, is discussed first and then a new allocation strategy using a Gray code (GC), called the GC strategy, is proposed. When processor relinquishment is not considered (i.e., static allocation), both of these strategies are proved to be optimal in the sense that each incoming request sequence is always assigned to a minimal subcube. It is also shown that the GC strategy outperforms the buddy strategy in detecting the availability of subcubes. Our results are extended further to implement an allocation strategy using more than one GC and derive the relationship between the GC's used and the corresponding ability of detecting the availability of various subcubes. The minimal number of GC's required for complete subcube recognition in a Q n is proved to be less than or equal to C [n/2] n. Several processor allocation strategies in a Q 5 are implemented on the NCUBE/six multiprocessor at the University of Michigan, and their performance is experimentally measured.