Marilynn Livingston

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A dominating set S of a graph G is perfect if each vertex of G is dominated by exactly one vertex in S. We study the existence and construction of PDSs in families of graphs arising from the interconnection networks of parallel computers. These include trees, dags, series-parallel graphs, meshes, tori, hypercubes, cube-connected cycles, cube-connected(More)
This paper examines the problem of locating and allocating large fault-free subsystems in multiuser massively parallel computer systems. Since the allocation schemes used in such large systems cannot allocate all possible subsystems a reduction in fault tolerance is experienced. We analyze the eeect of diierent allocation methods including the buddy and(More)
We consider the problem of determining the minimum number of faulty processors , n; m, and of faulty links, n; m, in an n-dimensional hypercube computer so that every m-dimensional subcube is faulty. Best known lower bounds for n; m and n; m are proved, several new recursive inequalities and new upper bounds are established, their asymptotic behavior for(More)
One important aspect of efficient use of a hypercube computer to solve a given problem is the assignment of subtasks to processors in such a way that the communication overhead is low. The subtasks and their inter-communication requirements can be modeled by a graph, and the assignment of subtasks to processors viewed as an embedding of the task graph into(More)
Cube-connected cycles are a family of cubic graphs with relatively small diameters and regular structure, making them attractive models for parallel architecture design. The existence of perfect dominating sets for any structural model of parallel computation is both useful for the construction of eecient algorithms for that structure and indicative of(More)
Large-scale ecological simulations are natural candidates for distributed discrete event simulation. In optimistic simulation of spatially explicit models, a difficult problem arises when individuals migrate between physical regions simulated by different logical processes. We present a solution to this problem that uses shared object states. Shared states(More)
This paper examines the problem of locating large fault-free subcubes in multiuser hypercube systems. We analyze a new location strategy, the cyclic buddy system, and compare its performance to the buddy system, the gray-coded buddy system, and several variants of them. We show that the cyclic buddy system gives a striking improvement in expected fault(More)