On the Three-Dimensional Channel Routing

Satoshi TAYU  Toshihiko TAKAHASHI  Eita KOBAYASHI  Shuichi UENO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.10   pp.1813-1821
Publication Date: 2016/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.1813
Type of Manuscript: PAPER
Category: Graphs and Networks
3-D channel,  NP-complete,  routing algorithm,  Steiner tree,  

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The 3-D channel routing is a fundamental problem on the physical design of 3-D integrated circuits. The 3-D channel is a 3-D grid G and the terminals are vertices of G located in the top and bottom layers. A net is a set of terminals to be connected. The objective of the 3-D channel routing problem is to connect the terminals in each net with a Steiner tree (wire) in G using as few layers as possible and as short wires as possible in such a way that wires for distinct nets are disjoint. This paper shows that the problem is intractable. We also show that a sparse set of ν 2-terminal nets can be routed in a 3-D channel with O(√ν) layers using wires of length O(√ν).