The Hardness of Minimum Capacity Network Design.pdfVIP

The Hardness of Minimum Capacity Network Design  David Peleg y and Herzl Regev z May Abstract We dene the Minimum Capacity Network Design problem MCND and present a taxonomy of its variants We consider all variants st their input do es not admit a general compressed form and prove that each such variant provided that it is not trivial is NPcomplete Intro duction This pap er is concerned with the Minimum Capacity Network Design MCND problem There is a very wide variety of network design problems In this pap er we are interested in the sort of the problems dened in KKG MP GJ problems NDNDND and other references therein contrary to some of these problems we are interested in solutions which induce general graphs rather than trees only The problem that we dene and consider here has a rather large numb er of variants in its own right The general setting involves a network of n interconnectable sites We dierentiate b etween variants that we call long ie ones whose instances and solutions are generally of p olynomial length in n and short variants whose instances and solutions are of length The results in this pap er are adapted from a part of Reg y Department of Applied Mathematics and Computer Science The Weizmann Institute Rehovot Israel Email pelegwisdomweizmann acil z Department of Applied Mathematics and Computer Science The Weizmann Institute Rehovot Israel Email tsellywisdomweizmannacil Supp orted in part by the Scholarship in Loving Memory of Jenny von Feinb erg p olylogarithmic in n We seek to characterize the minimal critical requirements that make a variant of the