Conflict graph

The graph shown in Figure 12(a) is called a conflict graph — nodes represent operations, and edges represent conflicts. For example. 

The initial data path is then optimized, coloring conflict graphs to minimize the number of functional units, registers, and multiplexors. 

The topography of the plant is represented by an undirected graph and consists of nodes and undirectional edges. The paths through the plant are represented by node lists, which are chronologically sorted by the point of time an AGV reaches the center of a node. Additionally the nodes include attributes which specify the points of time an AGV enters and leaves a node and the period of time which the AGV waits at the center of a node. These additional attributes are needed during the conflict resolution to model waiting, acceleration and deceleration of an AGV. 

Unfortunately, even these rules are not ready for use in an integrator tool as described in the previous section. In case of non-deterniinistic transformations between interdependent documents, it is crucial that the user is made aware of conflicts between applicable rules. A conflict occurs, if multiple rules match the same increment as owned increment. Thus, we have to consider all applicable rules and their mutual conflicts before selecting a rule for execution. To achieve this, we have to give up atomic rule execution, i.e., we have to decouple pattern matching from graph transformation [33, 255]. 

During the first phase (construct), all possible rule applications and conflicts between them are determined and stored in the graph. First, for each increment in the documents that has a type compatible with the dominant increment s type of any rule, a half link is created that references this increment. In the example, half links are created for the increments 11 and 13, and named LI and L2, respectively (cf. Fig. 3.33 a). 

Here, two types of conflicts can be found. First, the rules Rb and Rc share the same dominant increment. Second, the rules Ra and Rb share a normal increment. Both situations lead to conflicts because each increment may only be transformed by one rule as normal or dominant increment. To prepare conflictresolving user interaction, conflicts of the second type are explicitly marked in the graph by adding an edge-node-edge construct (e.g. 01 in Fig. 3.33 b). 

If no rule could be selected automatically, the user has to decide which rule is to be executed. Therefore, in the next step (find decisions), all conflicts are collected and presented to the user. For each half link, all possible rule applications are shown. If a rule application conflicts with another rule of a different half link, this is marked as annotation at both half links. Rules that are not executable due to a missing context are included in this presentation but cannot be selected for execution. This information allows the user to select a rule manually, knowing which other rule applications will be made impossible by his decision. The result of the user interaction (ask for user decision) is stored in the graph and the selected rule is executed in the execution phase. 

In [658], a consistency management approach for different view points [669] of development processes is presented. The formalism of distributed graph transformations [992] is used to model view points and their interrelations, especially consistency checks and repair actions. To the best of our knowledge, this approach works incrementally but does not support detection of conflicting rules and user interaction. 

Fang, L., Hipel, K. W., and Kilgour, D. M. (1993), Interactive Decision Making The Graph Model for Conflict Resolution, John Wiley Sons, New York. 

ABSTRACT The objective of the approach is to calculate the probability of a failure coincidence or maintenance conflict, respectively, in an -system-single-maintenance-unit scenario. Beside operation with conventional systems. Reliability-adaptive Systems can be considered as well in this scenario. The approach applies multiple integrals over products of probability density functions and discusses the permutation of coincidence patterns explicitly. So-called staple graph coincidence permutation diagrams and coincidence permutation trees are introduced as graphical representations. 

From optimization point of view it is desired that Us(x) < Uo during a mission time Tm, i-e. there is defined a maximal value of system unavailability that cannot be overstepped. System unavailabiUty function depends partly on graph structure and partly on component s unavailability functions. We will assume that the structure of AG, as well as component hazard rate is invariant system characteristics. On the other side, the other component characteristics, as Test intervals (Tls) or repair rates can be changed within a reasonable range. Just these component characteristics may he used as decision variables because they influence hoth conflicting functions, that is unavaUahility Us(x) and cost Cs (i.e. objective function/(x)). 

If derivative causality is assigned to the bond graph as preferred causality, (Fig. 3.1), then both storage elements take derivative causality. The resulting causal conflict at the right-hand 0-junction is resolved by turning the effort sensor into a flow sensor. 

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