Minimum Manhattan Network is NP-Complete

Routing with Minimum Wire Length in the Dogleg-Free Manhattan Model is NP-Complete

The present article concentrates on the dogleg-free Manhattan model where horizontal and vertical wire segments are positioned on different sides of the board and each net (wire) has at most one horizontal segment. While the minimum width can be found in linear time in the single row routing, apparently there was no efficient algorithm to find the minimum wire length. We show that there is no h...

Manhattan Channel Routing is NP-complete Under Truly Restricted Settings

Settling an open problem that is over ten years old, we show that Abstract-1 Manhattan channel routing—with doglegs allowed—is NP-complete when all nets have two terminals. This result fills the gap left by Szymanski [Szy85], who showed the NP-completeness for nets with four terminals. Answering a question posed by Schmalenbach [Sch90] and Greenberg, Jájá, and Krishnamurty [GJK92], we prove tha...

Bidirected minimum Manhattan network problem

In the bidirected minimum Manhattan network problem, given a set T of n terminals in the plane, we need to construct a network N (T) of minimum total length with the property that the edges of N (T) are axis-parallel and oriented in a such a way that every ordered pair of terminals is connected in N (T) by a directed Manhattan path. In this paper, we present a polynomial factor 2 approximation ...

Approximating a Minimum Manhattan Network

Overloading is NP - complete

We show that overloading is NP-complete. This solves exercise 6.25 in the 1986 version of the Dragon book.