Efficient allocation of chain-like task on chain-like network computers

Context-Aware Optimal Assignment of a Chain-Like Processing Task onto Chain-Like Resources in M-Health

“…Therefore, the assignment problem is translated into a path-search problem which can be solved with time complexity of O(m 3 n) and space complexity of O(m 2 n) ( [4]). Some improved algorithms are further reported in [5][6][7].…”

Task distribution based adaptation in mobile patient monitoring systems

“…Compared to earlier work, this new method relaxes a so-called contiguity constraint, which is a necessity in the earlier case but unnecessarily constraining MPMSs. Furthermore, we observed from our experiments that the assignment graph "construction" step is more time consuming than the actual "search" step in most of cases, which suggests that the evaluation on this kind of graph-based method should be based on the time complexity of the entire method instead of the "search" step only [Bok88,SC90,NO91]. Although this graph-based exact algorithm is more efficient compared to earlier work, it still has a major drawback on memory consumption: it requires an assignment graph to be constructed first, which is a bottleneck of the solution (Table 4.1).…”

“…This is, to the best our knowledge, the first experimental study based on series of theoretical studies on chain-chain assignment prob- One observation we made is that the "construction" step is more time consuming than the actual "search" step in most cases, which suggests that the evaluation on this kind of graph-based method should be based on the time complexity of the entire method instead of the "search" step only [Bok88,SC90,NO91]. Furthermore, we also implemented a program based on the optimal assignment approach proposed The CPU time of searching for the optimal chain-chain assignment by Bokhari [Bok88] and tested against our method with the contiguity constraint.…”

“…This procedure works by recursively computing the bottleneck processing time f ik when the first i tasks are optimally assigned to the first k processors. In [SC90], the authors proposed a new method to construct the task assignment graph with the number of edges of the order of O(m 2 n) but relax the full-use constraint.…”

“…Following the same weighting and search steps as the ones in the assignment problem without contiguity constraint, the optimal assignment with the contiguity constraint can be obtained by searching the shortest path in this new assignment graph. This new assignment graph has some sort of relation with some earlier proposed assignment graphs [SC90,HL92,Yeh05]: the vertex matrix in our solution is the transpose of the vertex matrix proposed earlier that represents the search space of task assignments with the contiguity constraint.…”