Journal of Computer and System Sciences
Asymptotically optimal algorithms for job shop scheduling and packet routing
Journal of Algorithms
Introduction to Linear Optimization
Introduction to Linear Optimization
Efficient PAC Learning for Episodic Tasks with Acyclic State Spaces
Discrete Event Dynamic Systems
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
Control Techniques for Complex Networks
Control Techniques for Complex Networks
Optimal flow control in acyclic networks with uncontrollable routings and precedence constraints
Discrete Event Dynamic Systems
| Hi-index | 0.00 |
The original definition of the problem of optimal node visitation (ONV) in acyclic stochastic digraphs concerns the identification of a routing policy that will enable the visitation of each leaf node a requested number of times, while minimizing the expected number of the graph traversals. The original work of Bountourelis and Reveliotis (2006) formulated this problem as a Stochastic Shortest Path (SSP) problem, and since the state space of this SSP formulation is exponentially sized with respect to the number of the target nodes, it also proposed a suboptimal policy that is computationally tractable and asymptotically optimal. This paper extends the results of Bountourelis and Reveliotis (2006) to the cases where (i) the tokens traversing the graph can "split" during certain transitions to a number of (sub-)tokens, allowing, thus, the satisfaction of many visitation requirements during a single graph traversal, and (ii) there are additional visitation requirements attached to the internal graph nodes, which, however, can be served only when the visitation requirements of their successors have been fully met. In addition, the presented set of results establishes stronger convergence properties for the proposed suboptimal policies, and it provides a formal complexity analysis of the considered ONV formulations. From a practical standpoint, the extension of the original results performed in this paper enables their effective usage in the application domains that motivated the ONV problem, in the first place.