Assigned:
Sunday, September 16, 2001
Due:
Friday, September 21, 2001
General Instructions
- Please review the
course information.
- You must write down with whom you worked on the assignment. If this
changes from problem to problem, then you should write down this
information separately with each problem.
- Numbered problems are all from the textbook Network Flows .
Problems
- Problem 4.24. Shortest path from 2 sources and 2 sinks. Try to
find a more elegant solution than finding four different shortest
paths and taking the smallest.
- Problem 4.26 and 4.27. Most vital arc.
- Problem 4.36. K shortest paths.
- Problem 4.42. Broken eggs.
- A sequence is bitonic if it monotonically
increases and then
monotonically decreases, or if it can be circularly shifted to
monotonically increase and then monotonically decrease. For example
the sequences (1,4,6,8,3,-2), (9,2,-4,-10,-5), and (1,2,3,4) are
bitonic, but
(1,3,12,4,2,10) is not bitonic.
Suppose that we are given a directed graph G=(V,E) with
real-valued edge lengths c,
and we wish to find single-source
shortest paths from a source vertex s. We are given one additional
piece of information: for each vertex v, the lengths of the
edges along any shortest path from s to v form a bitonic sequence.
Give the most efficient algorithm you can to solve this problem, and
analyze its running time.
Switch to:
cliff@ieor.columbia.edu