Honors Theory of Computation, Spring'00.

HOMEWORK 1:

Out: Jan 19
Due: Jan 31


1) Solve Problem 1.4.12 (Chapter 1, Papadimitriou's bk)

	IMPORTANT: you must answer the entire question in one page
	(with reasonable size handwriting).  When necessary,
	you must summarize the method or argument.

	FOR YOUR CONVENIENCE, HERE IS THE QUESTION:

	Show that, if in the augmentation algorithm of Section 1.2
	we always augment by a shortest path, then (a) the distance
	of a node from s cannot decrease from an N(f)
	to the next.  Furthermore, (b) if edge (i,j) is the
	bottleneck at one stage (i.e., it is the edge along the augmenting
	path with the smallest capacity), then the distance of i
	from s must increase before it becomes a bottleneck
	in the opposite direction.  (c) Conclude that there are at
	most O(|E|.|V|) augmentations.