algorithm - Most probable path taken to reach a particular node in graph -


we have system customer comes , interacts, triggers jobs , many actions. have 1000s of such users. each job has name , our backend database has data customer interactions.

these jobs fail often. know why particular job failed based on inputs, want find path taken user (journey) before reached failure job. want see if can improve experience before failure avoided.

example (hypothetical), login->create file-> save file -> download file. download file failing error. happens when save has completed. if have done operation between save file , download, down load not fail. hidden bug possibly.

the question - given history of 3000 users graph traversal (take paths of size 5 [as moving window]) build system when asked **

"what probable paths reach node x"

gives top 5 paths reach x.

i have created nodes [jobname][state], example, loginsuccess->createfilesuccess->savefilesuccess->downloadfailed. x typically [job name]failed node query. have 50 jobs , 3 states, success, failed cancelled.

any idea how build model, algorithm use, , how reverse generate probabilities when node asked?

adding more clarity -

given target node, can list probable paths reach length 5. dont know starting points start dijkstra's. direct path of low probability might exit given starting node, directly target node, need find paths of length 5.

the first step take construct list of records of length 5, each such record contains 5 steps taken particular customer leading node x. sort list , count number of times each possible record occurs in it, work out popular records.

another approach assign each edge exiting node score fraction of paths exited node exit via edge. compute overall score path multiplying scores edges, , again take observed paths highest scores.


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