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In this paper, we propose load distribution strategies for divisible loads for networked computing environments where computation and communication resource characteristics are unknown and/or vary with time. The principle on which our strategies are formulated is based on using probing loads to estimate the network characteristics and using them to determine the best possible load distribution. This work extends the adaptive strategies proposed in an earlier work to multilevel general networks. These networks, while being more challenging, also offer several opportunities that can be exploited to make the probing phase more efficient. We propose two strategies, one static, which caters to the presence of unknown parameters, and the other dynamic, which caters to both unknown as well as time-varying network parameters. The proposed strategies are robust, resilient, and easily adaptable to network fluctuations. The algorithms are also shown to have a tracking ability, a property that is important in dynamic environments. Examples are presented to illustrate the salient features of these strategies. [ABSTRACT FROM AUTHOR]

Alternating group graphs AGn, studied by Jwo and others, Constitute a class of Cayley graphs that possess certain desirable properties compared with other regular networks considered by researchers in parallel and distributed computing. A different form, ANn, of such graphs, proposed by Youhou and dubbed alternating group networks, has been shown to possess advantages over AGn. For example, ANn has a node degree that is smaller by a factor of about 2 while maintaining a diameter comparable to that of AGn, is maximally fault-tolerant, and shares some of the positive structural attributes of the well-known star graph. In this paper, we characterize the distance between any two nodes in ANn and present an optimal (shortest-path) routing algorithm for this class of networks. [ABSTRACT FROM AUTHOR]

This paper establishes the state of the art in both deterministic and randomized online permutation routing in the POPS network. Indeed, we show that any permutation can be routed online on a POPS(d, g) network either with O(d/g log g) deterministic slots, or, with high probability, with 5c[d/g] + o(d/g) + O(log log g) randomized slots, where constant c = exp(1 + e-1) ≈ 3.927. When d = ϴ(g), which we claim to be the ‘interesting’ case, the randomized algorithm is exponentially faster than any other algorithm in the literature, both deterministic and randomized ones. This is true in practice as well. Indeed, experiments show that it outperforms its rivals even starting from as small a network as a POPS(2, 2) and the gap grows exponentially with the size of the network. We can also show that, under proper hypothesis, no deterministic algorithm can asymptotically match its performance. [ABSTRACT FROM AUTHOR]

A Multiple Bus Network (MBN) connects a set of processors via a set of buses. Two important parameters of an MBN are its loading (largest number of connections on a bus) and its degree (largest number of connections to a processor). These parameters determine the cost, speed, and implementability of the MBN. The smallest degree that any useful MBN can have is 2. In this paper, we study the relationship between running time, degree, and loading of degree-2 MBNs running a fundamental class of algorithms called binary tree algorithms. (A binary tree algorithm reduces 2n inputs at the leaves of a balanced binary tree to a single result at the root of the tree.) Specifically, we establish a nontrivial Ω(n/log n) loading lower bound for any degree-2 MBN running a 2n input binary tree algorithm optimally in n steps. We show that this bound does not hold if the restriction on the degree or the running time is relaxed. That is, optimal-time, degree-3, constant loading MBNs and suboptimal-time, degree-2, constant loading MBNs exist for binary tree algorithms. We also derive a lower bound on the additional time (beyond the optimal) needed to run binary tree algorithms on a degree-2, loading-L MBN, for any L⩾ 3. [ABSTRACT FROM AUTHOR]