This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CMSC 451: MaxFlow Extensions Slides By: Carl Kingsford Department of Computer Science University of Maryland, College Park Based on Section 7.7 of Algorithm Design by Kleinberg & Tardos. Circulations with Demands • Suppose we have multiple sources and multiple sinks. • Each sink wants to get a certain amount of flow (its demand ). • Each source has a certain amount of flow to give (its supply ). • We can represent supply as negative demand . Demand Example 1 2 5 3 4 6 8 9 7 5 3 2 4 14 11 9 7 4 3 4 10 3 demand d 5 = 3 supply d 1 = 4 supply d 2 = 7 d 8 = 8 d 4 = 0 Constraints Goal: find a flow f that satisfies: 1 Capacity constraints : For each e ∈ E , 0 ≤ f ( e ) ≤ c e . 2 Demand constraints : For each v ∈ V , f in ( v ) f out ( v ) = d v . The demand d v is the excess flow that should come into node. Sources and Sinks Let S be the set of nodes with negative demands (supply). Let T be the set of nodes with positive demands (demand). In order for there to be a feasible flow, we must have: X s ∈ S d s = X t ∈ T d t Let D = ∑ t ∈ T d t . Reduction How can we turn the circulation with demands problem into the maximum flow problem? Reduction...
View
Full
Document
This note was uploaded on 01/13/2012 for the course CMSC 423 taught by Professor Staff during the Fall '07 term at Maryland.
 Fall '07
 staff

Click to edit the document details