NP-Completeness and an Approximation Algorithm for Rectangle Escape Problem With Application to PCB Routing

Research output: Contribution to journalJournal articlepeer-review

13 Citations (Scopus)


In this paper, we introduce and study the rectangle escape problem (REP), which is motivated by printed circuit board (PCB) bus escape routing. Given a rectangular region R and a set S of rectangles within R, the REP is to choose a direction for each rectangle to escape to the boundary of R, such that the resultant maximum density over R is minimized. We prove that the REP is NP-complete, and show that it can be formulated as an integer linear programming (ILP). A provably good approximation algorithm for the REP is developed by applying linear programming (LP) relaxation and a special rounding technique to the ILP. In addition, an iterative refinement procedure is proposed as a postprocessing step to further improve the results. Our approximation algorithm is also shown to work for more general versions of REP: weighted REP and simultaneous REP. Our approach is tested on a set of industrial PCB bus escape routing problems. Experimental results show that the optimal solution can be obtained within several seconds for each of the test cases.
Original languageEnglish
Article number6269973
Pages (from-to)1356-1365
Number of pages10
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Issue number9
Publication statusPublished - 16 Aug 2012

User-Defined Keywords

  • Routing
  • Approximation algorithms
  • Approximation methods
  • Algorithm design and analysis
  • Printed circuits
  • Linear programming
  • Approximation algorithm
  • linear programming relaxation
  • NP-completeness
  • printed circuit board (PCB) routing


Dive into the research topics of 'NP-Completeness and an Approximation Algorithm for Rectangle Escape Problem With Application to PCB Routing'. Together they form a unique fingerprint.

Cite this