mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

a process graph or P-graph is a

directed Director may refer to: Literature * ''Director'' (magazine), a British magazine * ''The Director'' (novel), a 1971 novel by Henry Denker * ''The Director'' (play), a 2000 play by Nancy Hasty Music * Director (band), an Irish rock band * ''Di ...

bipartite graph In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V, that is every edge connects a vertex in U to one in V. Vertex sets U and V are ...

used in

workflow A workflow consists of an orchestrated and repeatable pattern 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 sequence of ...

modeling A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...

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 discre ...

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

disjunctive Disjunctive can refer to: * Disjunctive population, in population ecology, a group of plants or animals disconnected from the rest of its range * Disjunctive pronoun * Disjunctive set * Disjunctive sequence * Logical disjunction In logic, d ...

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 Edge or EDGE may refer to: Technology Computing * Edge computing, a network load-balancing system * Edge device, an entry point to a computer network * Adobe Edge, a graphical development application * Microsoft Edge, a web browser developed by ...

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