mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

a process graph or P-graph is a

directed Direct may refer to: Mathematics * Directed set, in order theory * Direct limit of (pre), sheaves * Direct sum of modules, a construction in abstract algebra which combines several vector spaces Computing * Direct access (disambiguation), a ...

bipartite graph In the mathematics, mathematical field of graph theory, a bipartite graph (or bigraph) is a Graph (discrete mathematics), graph whose vertex (graph theory), vertices can be divided into two disjoint sets, disjoint and Independent set (graph theo ...

used in

workflow Workflow is a generic term for orchestrated and repeatable patterns of activity, enabled by the systematic organization of resources into processes that transform materials, provide services, or process information. It can be depicted as a seque ...

modeling A model is an informative representation of an object, person, or system. The term originally denoted the Plan_(drawing), plans of a building in late 16th-century English, and derived via French language, French and Italian language, Italian ult ...

Description

With a process graph, the vertices of the

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discret ...

are of two types, operation (O) and material (M). These vertex types form two disjunctive

set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...

s. The edges of the graph link the O and M vertices. An edge from an operation vertex (O) connects to a material vertex (M) if M is the output of O, such as a 'document' (material) that is output by a 'write-up' (operation). An edge from M to O indicates that M is an element of the input set of O, e.g. a document may be part of the input to a 'review' operation.

Applications

Process-graph is in use in different fields of application in Process Network Synthesis (PNS) . An example for an application is

Process Network Synthesis Process network synthesis (PNS) is a method to represent a process structure in a 'directed bipartite graph'. Process network synthesis uses the P-graph method to create a process structure. The scientific aim of this method is to find optimum stru ...

. The method is in scientific use to find optimum process chains in chemical formulas, energy technology networks and other optimisation problems like evacuation routes in buildings or transportation routes. Process graphs are also used in understanding the control flow of multi-threaded processes. If there are n concurrent threads running, a process graph models the execution of n concurrent threads and their trajectories through an n dimensional Cartesian plane. The origin of the graph corresponds to the initial state where none of the threads have completed an instruction. Each directed edge corresponds to the execution of an instruction and transition to other. Valid edges can either go up or right because programs cannot run backward for the edges to left or down. Since two threads can't complete the same instruction at the same time, diagonal edges are not allowed.

References

External links

P-Graph wiki

Process Network Synthesis Problem Definition
{{DEFAULTSORT:Process Graph Application-specific graphs