A global router based on a multicommodity flow model
Integration, the VLSI Journal
Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Two Steiner tree packing problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Packing Steiner trees: a cutting plane algorithm and computational results
Mathematical Programming: Series A and B
Packing Steiner Trees: Separation Algorithms
SIAM Journal on Discrete Mathematics
Coordination complexity of parallel price-directive decomposition
Mathematics of Operations Research
The Steiner tree packing problem in VLSI design
Mathematical Programming: Series A and B
Randomized metarounding (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On the inapproximability of disjoint paths and minimum Steiner forest with bandwidth constraints
Journal of Computer and System Sciences
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
IEEE/ACM Transactions on Networking (TON)
Algorithms for VLSI Physcial Design Automation
Algorithms for VLSI Physcial Design Automation
A branch-and-price algorithm for the Steiner tree packing problem
Computers and Operations Research
Provably Good Global Routing of Integrated Circuits
SIAM Journal on Optimization
Towards a Practical Volumetric Cutting Plane Method for Convex Programming
SIAM Journal on Optimization
Heuristic algorithms for packing of multiple-group multicasting
Computers and Operations Research
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Hardness of the Steiner Tree Problem on Graphs
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
New modeling and optimization techniques for the global routing problem
New modeling and optimization techniques for the global routing problem
Minimum k Arborescences with Bandwidth Constraints
Algorithmica
An Approximate Max-Steiner-Tree-Packing Min-Steiner-Cut Theorem
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Integer Linear Programming Models for Global Routing
INFORMS Journal on Computing
Mathematical Programming: Series A and B
Packing trees in communication networks
WINE'05 Proceedings of the First international conference on Internet and Network Economics
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Implementation of approximation algorithms for the multicast congestion problem
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Research: A group multicast routing algorithm by using multiple minimum Steiner trees
Computer Communications
GRIP: scalable 3D global routing using integer programming
Proceedings of the 46th Annual Design Automation Conference
Confidentiality preserving integer programming for global routing
Proceedings of the 49th Annual Design Automation Conference
Hi-index | 0.04 |
In this paper, we study the global routing problem in VLSI design and the multicast routing problem in communication networks. First we propose new and realistic models for both problems. In the global routing problem in VLSI design, we are given a lattice graph and subsets of the vertex set. The goal is to generate trees spanning these vertices in the subsets to minimize a linear combination of overall wirelength (edge length) and the number of bends of trees with respect to edge capacity constraints. In the multicast routing problem in communication networks, a graph is given to represent the network, together with subsets of the vertex set. We are required to find trees to span the given subsets and the overall edge length is minimized with respect to capacity constraints. Both problems are APX-hard. We present the integer linear programming (LP) formulation of both problems and solve the LP relaxations by the fast approximation algorithms for min-max resource-sharing problems in [K. Jansen, H. Zhang, Approximation algorithms for general packing problems and their application to the multicast congestion problem, Math. Programming, to appear, doi:10.1007/s10107-007-0106-8] (which is a generalization of the approximation algorithm proposed by Grigoriadis and Khachiyan [Coordination complexity of parallel price-directive decomposition, Math. Oper. Res. 2 (1996) 321-340]). For the global routing problem, we investigate the particular property of lattice graphs and propose a combinatorial technique to overcome the hardness due to the bend-dependent vertex cost. Finally, we develop asymptotic approximation algorithms for both problems with ratios depending on the best known approximation ratio for the minimum Steiner tree problem. They are the first known theoretical approximation bound results for the problems of minimizing the total costs (including both the edge and the bend costs) while spanning all given subsets of vertices.