Online Assignment Algorithms for Dynamic Bipartite Graphs

This paper analyzes the problem of assigning weights to edges incrementally in a dynamic complete bipartite graph consisting of producer and consumer nodes. The objective is to minimize the overall cost while satisfying certain constraints. The cost and constraints are functions of attributes of the edges, nodes and online service requests. Novelty of this work is that it models real-time distributed resource allocation using an approach to solve this theoretical problem. This paper studies variants of this assignment problem where the edges, producers and consumers can disappear and reappear or their attributes can change over time. Primal-Dual algorithms are used for solving these problems and their competitive ratios are evaluated

Minimum-cost multicast over coded packet networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved

A manpower utilization model for a Naval Air Rework Facility

The management personnel at the Naval Air Rework Facility, North Island Naval Air Station, San Diego, California, are currently faced with two difficult planning problems inherent in any large industrial concern. These are the inability to smooth out the workload so that it may be considered constant over a specific period of time and the determination of the optimal utilization of the direct labor force in order to produce the workload and minimum dollar wage cost. Assuming a constant workload, a mathematical model of this utilization problem, incorporating constraints and restrictions placed upon NARFSD by various agencies, is developed which can be solved as a minimal cost flow-with-gains network problem. By varying the constraint and restriction limits, several alternative manpower utilization options and their related costs are examined. Finally, various methods of smoothing variable workloads are suggested.http://archive.org/details/manpowerutilizat00clifLieutenant, United States NavyApproved for public release; distribution is unlimited