Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
A faster strongly polynomial minimum cost flow algorithm
Operations Research
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Improved Algorithms for Bipartite Network Flow
SIAM Journal on Computing
Efficient Algorithms for the Hitchcock Transportation Problem
SIAM Journal on Computing
Recent directions in netlist partitioning: a survey
Integration, the VLSI Journal
Algorithms for large-scale flat placement
DAC '97 Proceedings of the 34th annual Design Automation Conference
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
A flat, timing-driven design system for a high-performance CMOS processor chipset
Proceedings of the conference on Design, automation and test in Europe
An effective congestion driven placement framework
Proceedings of the 2002 international symposium on Physical design
Improved Approximation Schemes for Scheduling Unrelated Parallel Machines
Mathematics of Operations Research
Optimality of Nested Partitions and Its Application to Cluster Analysis
SIAM Journal on Optimization
PROUD: A Sea-Of-Gates Placement Algorithm
IEEE Design & Test
ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
Journal of Computer and System Sciences
New theoretical results on quadratic placement
Integration, the VLSI Journal
A faster polynomial algorithm for the unbalanced Hitchcock transportation problem
Operations Research Letters
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We consider the following problem: given a set of points in the plane, each with a weight, and capacities of the four quadrants, assign each point to one of the quadrants such that the total weight of points assigned to a quadrant does not exceed its capacity, and the total distance is minimized. This problem is most important in placement of VLSI circuits and is likely to have other applications. It is NP-hard, but the fractional relaxation always has an optimal solution which is ''almost'' integral. Hence for large instances, it suffices to solve the fractional relaxation. The main result of this paper is a linear-time algorithm for this relaxation. It is based on a structure theorem describing optimal solutions by so-called ''American maps'' and makes sophisticated use of binary search techniques and weighted median computations. This algorithm is a main subroutine of a VLSI placement tool that is used for the design of many of the most complex chips.