A global router based on a multicommodity flow model

Shragowitz, Eugene; Keel, S.

doi:10.1016/s0167-9260(87)80003-2

Cited by 70 publications

(24 citation statements)

References 8 publications

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“…For a given [21] for background on multicommodity flows). We add the constraint that each vertex of G can be in at most one Steiner tree, and require that the flow of commodity i can only be routed through vertices in Steiner tree S i .…”

Section: Routingmentioning

confidence: 99%

Discrete optimization using quantum annealing on sparse Ising models

et al. 2014

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This paper discusses techniques for solving discrete optimization problems using quantum annealing. Practical issues likely to affect the computation include precision limitations, finite temperature, bounded energy range, sparse connectivity, and small numbers of qubits. To address these concerns we propose a way of finding energy representations with large classical gaps between ground and first excited states, efficient algorithms for mapping non-compatible Ising models into the hardware, and the use of decomposition methods for problems that are too large to fit in hardware. We validate the approach by describing experiments with D-Wave quantum hardware for low density parity check decoding with up to 1000 variables.

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Section: Routingmentioning

confidence: 99%

Discrete optimization using quantum annealing on sparse Ising models

et al. 2014

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“…The main contribution of the paper is a provably good algorithm for these generalizations of the MTMCF problem. Prior to our work, heuristics based on solving fractional relaxations of integer multicommodity flow formulations have been applied to VLSI global routing [15], [20], [2], [11], [1]. As noted in [14], the applicability of this approach is limited to problem instances of relatively small size by the prohibitive cost of solving exactly the fractional relaxation.…”

Section: Givenmentioning

confidence: 99%

Provably good global buffering by generalized multiterminal multicommodity flow approximation

Dragan

Kahng

Măndoiu

et al. 2002

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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“…Linear programming methods have been used to select the assignment of segments in 2, 22 , in order to minimize the maximum density across a channel. Related to the LP methods are those based on network ow o r m ulticommodity o w models 30,36,7,34 . In 20 , the authors use path-based timing constraints and utilize the features speci c to bipolar design to optimize both the delay and area of the global routing result.…”

Section: Introductionmentioning

confidence: 99%

Performance driven global routing for standard cell design

Cong

Madden

1997

Proceedings of the 1997 International Symposium on Physical Design - ISPD '97

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Advances in fabrication technology have resulted in a continual shrinkage of device dimensions. This has resulted in smaller device delays, greater resistance along interconnect wires, and a greater impact of interconnect on total system performance. These changes have driven a considerable number of studies on single-net interconnect optimization, but relatively little work has been done to integrate the results on single-net optimization with the problem of global routing and interconnect optimization for the entire circuit. In this paper, we present the DECIMATE global router for performance driven standard cell design. The router applies both interconnect topology optimization and variable-width wire sizing optimization results to the global routing problem, while maintaining routing areas that are comparable with TimberWolf Systems' well-known commercial global router. Optimal selection of interconnection structures is shown to be an NP-Hard problem; we provide a simple heuristic for the problem, and show that it is e ective with experiments on industry benchmarks. Under the Elmore delay model, our global router produces as much as a 35 reduction in critical path delay o v er TimberWolf Systems' global router, while path length reductions are as large as 52. Circuit area optimization is performed taking into account v ariably-sized wires, xed routing topologies, and pre-existing obstacles; an improved cost function obtains as much as an 11.6 reduction in channel density o v er the result in 16 .

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A global router based on a multicommodity flow model

Cited by 70 publications

References 8 publications

Discrete optimization using quantum annealing on sparse Ising models

Discrete optimization using quantum annealing on sparse Ising models

Provably good global buffering by generalized multiterminal multicommodity flow approximation

Performance driven global routing for standard cell design

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