On the König deficiency of zero-reducible graphs

A confluent and terminating reduction system is introduced for graphs,which preserves the number of their perfect matchings. A union-find algorithm is presented to carry out reduction in almost linear time. The König property is investigated in the context of reduction by introducing the König deficiency of a graph G as the difference between the vertex covering number and thematching number ofG. It is shown that the problem of finding the König deficiency of a graph is NP-complete even if we know that the graph reduces to the empty graph. Finally, the König deficiency of graphs G having a vertex v such that G − v has a unique perfect matching is studied in connection with reduction

Planning automated guided vehicle movements in a factory

This dissertation examines the problems of planning automated guided vehicle (AGV) movement schedules in an automated factory. AGVs are used mainly for material delivery and will have an important role in linking "islands of automation" in automated factories. Their employment in this context requires the plans to be generated in a manner which supports temporal projection so that further planning in other areas is possible. Planning also occurs in a dynamic scenario—while some plans are being executed, planning for new tasks and replanning failing plans occur. Expeditious planning is thus important so that deadlines can be met. Furthermore, dynamic replanning in a multi-agent environment has repercussions—changing one plan may require revision of other plans. Hence the issue of limiting the side effects of dynamic replanning is also considered. In dealing with these issues, the goals of this research are: (1) generate movement plans which can be executed efficiently; (2) develop fast algorithms for the recurrent subproblems viz. task assignment and route planning; and (3) generate robust plans which tolerate execution deviations; this helps to minimize disruptive dynamic replanning with its tendency to initiate a chain reaction of plan revisions. Efficient movement plans mean more productive utilization of the AGV fleet and this objective can be realized by three approaches. First, the tasks are assigned to AGVs optimally using an improved implementation of the Hungarian method. Second, the planner computes shortest routes for the AGVs using a bidirectional heuristic search algorithm which is amenable to parallel implementation for further computational time reduction. Third, whenever AGVs are fortuitously predisposed to assist each other in task execution, the planner will generate gainful collaborative plans. Efficient algorithms have been developed in these areas. The algorithms for task assignment and route planning are also designed to be fast, in keeping with the objective of expeditious planning. Robust plans can be generated using the approach of tolerant planning. Robustness is achieved in two ways: (1) by being tolerant of an AGV's own execution deviations; and (2) by being tolerant of other AGVs' deviant behaviour. Tolerant planning thus defers dynamic replanning until execution errors become excessive. The underlying strategy is to provide more than ample resources (time) for AGVs to achieve various subgoals. Such redundancies aggravate the resource contention problem. To solve this, an iterative negotiation model is proposed. During negotiations, AGVs yield in turn to help eliminate the conflict. The negotiation behaviour of each is governed by how much spare resources each has and tends towards intransigence as the bottom line is approached. In this way, no AGV will jeopardize its own plan while cooperating in the elimination of conflicts. By gradual yielding, an AGV is also able to influence the other party to yield more if it can, therein achieving some fairness. The model has many of the characteristics of negotiation acts in the real world (e.g. skilful negotiation, intransigence, selfishness, willingness to concede, nested negotiations)