1 / 17

CSE 421 Algorithms

Explore various applications of network flow, including airplane scheduling, image segmentation, and baseball elimination. Learn how network flow algorithms can be applied to solve these problems effectively.

cspencer
Download Presentation

CSE 421 Algorithms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CSE 421Algorithms Richard Anderson Lecture 27 Network Flow Applications

  2. Today’s topics • More network flow reductions • Airplane scheduling • Image segmentation • Baseball elimination

  3. Airplane Scheduling • Given an airline schedule, and starting locations for the planes, is it possible to use a fixed set of planes to satisfy the schedule. • Schedule • [segments] Departure, arrival pairs (cities and times) • Approach • Construct a circulation problem where paths of flow give segments flown by each plane

  4. Compatible segments • Segments S1 and S2 are compatible if the same plane can be used on S1 and S2 • End of S1 equals start of S2, and enough time for turn around between arrival and departure times • End of S1 is different from S2, but there is enough time to fly between cities

  5. Graph representation • Each segment, Si, is represented as a pair of vertices (di, ai, for departure and arrival), with an edge between them. • Add an edge between ai and dj if Si is compatible with Sj. di ai ai dj

  6. Setting up a flow problem 1,1 di ai 0,1 ai dj 1 -1 P’i Pi

  7. Result • The planes can satisfy the schedule iff there is a feasible circulation

  8. Image Segmentation • Separate foreground from background

  9. Image analysis • ai: value of assigning pixel i to the foreground • bi: value of assigning pixel i to the background • pij: penalty for assigning i to the foreground, j to the background or vice versa • A: foreground, B: background • Q(A,B) = S{i in A}ai + S{j in B}bj - S{(i,j) in E, i in A, j inB}pij

  10. Pixel graph to flow graph s t

  11. Mincut Construction s av pvu u v puv bv t

  12. Baseball elimination • Can the Dung Beetles win the league? • Remaining games: • AB, AC, AD, AD, AD, BC, BC, BC, BD, CD

  13. Baseball elimination • Can the Fruit Flies win the league? • Remaining games: • AC, AD, AD, AD, AF, BC, BC, BC, BC, BC, BD, BE, BE, BE, BE, BF, CE, CE, CE, CF, CF, DE, DF, EF, EF

  14. Assume Fruit Flies win remaining games • Fruit Flies are tied for first place if no team wins more than 19 games • Allowable wins • Ants (2) • Bees (3) • Cockroaches (3) • Dung Beetles (5) • Earthworms (5) • 18 games to play • AC, AD, AD, AD, BC, BC, BC, BC, BC, BD, BE, BE, BE, BE, CE, CE, CE, DE

  15. Remaining games • AC, AD, AD, AD, BC, BC, BC, BC, BC, BD, BE, BE, BE, BE, CE, CE, CE, DE s AC AD BC BD BE CE DE E A B C D T

  16. Network flow applications summary • Bipartite Matching • Disjoint Paths • Airline Scheduling • Survey Design • Baseball Elimination • Project Selection • Image Segmentation

More Related