 
Summary: To appear in Proc. 27'th ACM Symposium on Theory Of Computing (STOC), May 1995 1
Improved Approximation Guarantees for MinimumWeight kTrees and
PrizeCollecting Salesmen
Baruch Awerbuch \Lambda Yossi Azar y Avrim Blum z Santosh Vempala z
Abstract
Consider a salesperson that must sell some quota
of brushes in order to win a trip to Hawaii. This
salesperson has a map (a weighted graph) in which
each city has an attached demand specifying the
number of brushes that can be sold in that city.
What is the best route to take to sell the quota
while traveling the least distance possible? Notice
that unlike the standard traveling salesman prob
lem, not only do we need to figure out the order
in which to visit the cities, but we must decide
the more fundamental question: which cities do
we want to visit?
In this paper we give the first approximation al
gorithms with polylogarithmic performance guar
antees for this problem, as well as for the slightly
