Abstract
We introduce a new method for Rectilinear Steiner Tree (RST) construction in a graph, using answer set programming. This method provides a formal representation of the problem as a logic program whose answer sets correspond to solutions. The answer sets for a logic program can be computed by special systems called answer set solvers. We describe the method for RST construction in the context of VLSI routing where multiple pins in a given placement of a chip are connected by an RST. Our method is different from the existing methods mainly in three ways. First, it always correctly determines whether a given RST routing problem is solvable, and it always produces a solution if one exists. Second, some enhancements of the basic problem, in which lengths of wires connecting the source pin to sink pins are restricted, can be easily represented by adding some rules. Our method guarantees to find a tree if one exists, even when the total wire length is not minimum. Third, routing problems with the presence of obstacles can be solved. With this approach, we have computed solutions to some RST routing problems using the answer set solver CMODELS.
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References
Hanan, M.: On Steiner’s problem with rectilinear distance. SIAM Journal on Applied Mathematics 14, 255–265 (1966)
Garey, M.R., Johnson, D.S.: The rectilinear Steiner tree problem is NP complete. SIAM Journal of Applied Mathematics 32, 826–834 (1977)
Marek, V., Truszczyński, M.: Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm: a 25-Year Perspective, pp. 375–398 (1999)
Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intelligence 138, 181–234 (2002)
Lifschitz, V.: Answer set programming and plan generation. Artificial Intelligence 138, 39–54 (2002)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Logic Programming: Proc. of the Fifth Int’l Conference and Symposium, pp. 1070–1080 (1988)
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385 (1991)
Hanan, M.: Net wiring for large scale integrated circuits. Tech. report, IBM (1965)
Lengauer, T.: Combinatorial Algorithms for Integrated Circuit Design (1990)
Nielsen, B.K., Winter, P., Zachariasen, M.: An exact algorithm for the uniformlyoriented steiner tree problem. In: Proc. of ESA, vol. 10, pp. 760–771 (2002)
Zhou, H.: Efficient steiner tree construction based on spanning graphs. In: ACM Int’l Symposium on Physical Design (2003)
Warme, D.M.: A new exact algorithm for rectilinear steiner trees. In: The Int’l Symposium on Mathematical Programming (1997)
Zachariasen, M.: Rectilinear full steiner tree generation. Networks 33, 125–143 (1999)
Ganley, J.L., Cohoon, J.P.: Routing a multi-terminal critical net: Steiner tree construction in the presence of obstacles. In: Proc. of the Int’l Symposium on Circuits and Systems, pp. 113–116 (1994)
McCarthy, J.: Elaboration tolerance (1999) (in progress)
Erdem, E., Lifschitz, V.: Tight logic programs. Theory and Practice of Logic Programming 3, 499–518 (2003)
Lloyd, J.: Foundations of Logic Programming (1984)
Lierler, Y., Maratea, M.: Cmodels-2: SAT-based answer sets solver enhanced to non-tight programs. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 346–350. Springer, Heidelberg (2003)
Erdem, E., Lifschitz, V., Wong, M.: Wire routing and satisfiability planning. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 822–836. Springer, Heidelberg (2000)
Erdem, E.: Theory and Applications of Answer Set Programming. PhD thesis, University of Texas at Austin, Department of Computer Sciences (2002)
East, D., Truszczyński, M.: More on wire routing with ASP. In: Working Notes of the AAAI Spring Symposium on Answer Set Programming (2001)
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Erdem, E., Wong, M.D.F. (2004). Rectilinear Steiner Tree Construction Using Answer Set Programming. In: Demoen, B., Lifschitz, V. (eds) Logic Programming. ICLP 2004. Lecture Notes in Computer Science, vol 3132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27775-0_27
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DOI: https://doi.org/10.1007/978-3-540-27775-0_27
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