The Maximum Cut Problem

International audience We introduce a new graph parameter that measures fractional covering of a graph by cuts. Besides being interesting in its own right, it is useful for study of homomorphisms and tension-continuous mappings. We study the relations with chromatic number, bipartite density, and other graph parameters. We find the value of our parameter for a family of graphs based on hypercubes. These graphs play for our parameter the role that cliques play for the chromatic number and Kneser graphs for the fractional chromatic number. The fact that the defined parameter attains on these graphs the correct value suggests that our definition is a natural one. In the proof we use the eigenvalue bound for maximum cut and a recent result of Engström, Färnqvist, Jonsson, and Thapper [An approximability-related parameter on graphs – properties and applications, DMTCS vol. 17:1, 2015, 33–66]. We also provide a polynomial time approximation algorithm based on semidefinite programming and in particular on vector chromatic number (defined by Karger, Motwani and Sudan [Approximate graph coloring by semidefinite programming, J. ACM 45 (1998), no. 2, 246–265]).

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Maximum cut in fuzzy nature: Models and algorithms

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2009.12.022 ◽

2010 ◽

Vol 234 (1) ◽

pp. 240-252 ◽

Cited By ~ 4

Author(s):

Rui-Sheng Wang ◽

Li-Min Wang

Keyword(s):

Maximum Cut

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Smoothed Analysis of the Squared Euclidean Maximum-Cut Problem

Algorithms - ESA 2015 - Lecture Notes in Computer Science ◽

10.1007/978-3-662-48350-3_43 ◽

2015 ◽

pp. 509-520 ◽

Cited By ~ 1

Author(s):

Michael Etscheid ◽

Heiko Röglin

Keyword(s):

Smoothed Analysis ◽

Maximum Cut

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Design and Investigation of a Dual Material Gate Arsenic Alloy Heterostructure Junctionless TFET with a Lightly Doped Source

Applied Sciences ◽

10.3390/app9194104 ◽

2019 ◽

Vol 9 (19) ◽

pp. 4104 ◽

Cited By ~ 2

Author(s):

Haiwu Xie ◽

Hongxia Liu ◽

Shupeng Chen ◽

Tao Han ◽

Shulong Wang

Keyword(s):

Integrated Circuit ◽

Lattice Mismatch ◽

Ultra Low Power ◽

Maximum Cut ◽

Novel Structure ◽

Power Integrated Circuit ◽

Polarization Electric Field ◽

Source Voltage ◽

Rf Performance ◽

Dual Material

This paper designs and investigates a novel structure of dual material gate-engineered heterostructure junctionless tunnel field-effect transistor (DMGE-HJLTFET) with a lightly doped source. Similar to the conventional HJLTFET, the proposed structure still adopts an InAs/GaAs0.1Sb0.9 heterojunction at source and channel interface and employs a polarization electric field at the arsenic heterojunction induced by the lattice mismatch in the InAs and GaAs0.1Sb0.9 zinc blende crystal to improve band to band tunneling (BTBT) current. However, the gate electrode is divided into three parts in DMGE-HJLTFET namely the auxiliary gate (M1), control gate (M2) and tunnel gate (M3) with workfunctions ΦM1, ΦM2 and ΦM3, where ΦM1 = ΦM3 < ΦM2, which not only improves ON-state current but also decreases the OFF-state current. In addition, a lightly doped source is used to further decrease the OFF-state current of this device. Simulation results indicate that DMGE-HJLTFET provides superior metrics in terms of logic and analog/radio frequency (RF) performance as compared with conventional HJLTFET, the maximum ON-state current and transconductance of the DMGE-HJLTFET increases up to 5.46 × 10−4 A/μm and 1.51 × 10−3 S/μm at 1.0 V drain-to-source voltage (Vds). Moreover, average subthreshold swing (SSave) of DMGE-HJLTFET is as low as 15.4 mV/Dec at low drain voltages. Also, DMGE-HJLTFET could achieve a maximum cut-off frequency (fT) of 423 GHz at 0.92 V gate-to-source voltage (Vgs) and a maximum gain bandwidth (GBW) of 82 GHz at Vgs = 0.88 V, respectively. Therefore, it has great potential in future ultra-low power integrated circuit applications.

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