Network flow

(a) Consider the following flow network with current flow fi and capacity ci of each edge i denoted by f: 0:3 2:5 2: 2 2:2 0:3 0:4 Draw the residual (di)graph. 3 marks] (b) Find an augmenting path (in the residual graph) for the previous question. How much more 2 marks] (c) We are organizing a conference where researchers present articles they have written. Re searchers (set A) who want to present an article send a paper to the conference organizers The conference organizers have access to a committee of reviewers (set B) who are each l ing to read up n articles each. Each paper submission gets reviewed by up to m reviewers. Moreover, each submission has a particular topic and each reviewer has a specialization for a set of topics, so papers on a given topic only get reviewed by those reviewers who are experts flow do we get from s to t? on that topic. The conference organizers need to decide whi reviewers will revi article (or equivalently, which articles will be reviewed by which reviewers). Explain how we 5 marks] can use network flow to solve this problem (a) Consider the following flow network with current flow fi and capacity ci of each edge i denoted by f: 0:3 2:5 2: 2 2:2 0:3 0:4 Draw the residual (di)graph. 3 marks] (b) Find an augmenting path (in the residual graph) for the previous question. How much more 2 marks] (c) We are organizing a conference where researchers present articles they have written. Re searchers (set A) who want to present an article send a paper to the conference organizers The conference organizers have access to a committee of reviewers (set B) who are each l ing to read up n articles each. Each paper submission gets reviewed by up to m reviewers. Moreover, each submission has a particular topic and each reviewer has a specialization for a set of topics, so papers on a given topic only get reviewed by those reviewers who are experts flow do we get from s to t? on that topic. The conference organizers need to decide whi reviewers will revi article (or equivalently, which articles will be reviewed by which reviewers). Explain how we 5 marks] can use network flow to solve this