Doubly Balanced Connected Graph Partitioning

Soltan, Saleh; Yannakakis, Mihalis; Zussman, Gil

doi:10.1137/1.9781611974782.126

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…Finally, in [46], the hardness of C-Max-2-Cut with the additional requirement that the supplies in both parts are balanced is analyzed. This has an application in power grid islanding, which is used to soften propagating failures.…”

Section: Related Literaturementioning

confidence: 99%

Mixed-integer programming techniques for the connected max-k-cut problem

et al. 2020

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We consider an extended version of the classical Max-$$k$$ k -Cut problem in which we additionally require that the parts of the graph partition are connected. For this problem we study two alternative mixed-integer linear formulations and review existing as well as develop new branch-and-cut techniques like cuts, branching rules, propagation, primal heuristics, and symmetry breaking. The main focus of this paper is an extensive numerical study in which we analyze the impact of the different techniques for various test sets. It turns out that the techniques from the existing literature are not sufficient to solve an adequate fraction of the test sets. However, our novel techniques significantly outperform the existing ones both in terms of running times and the overall number of instances that can be solved.

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Section: Related Literaturementioning

confidence: 99%

Mixed-integer programming techniques for the connected max-k-cut problem

et al. 2020

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Doubly Balanced Connected Graph Partitioning

Soltan

Yannakakis

Zussman

2020

ACM Trans. Algorithms

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We introduce and study the Doubly Balanced Connected graph Partitioning (DBCP) problem: Let G=(V, E) be a connected graph with a weight (supply/demand) function p:|V2| , |V2| |V1| }≤c s , for some constants c p and c s . When G is 2-connected, we show that a solution with c p =1 and c s =3 always exists and can be found in polynomial time. Moreover, when G is 3-connected, we show that there is always a 'perfect' solution (a partition with p(V 1 )=p(V 2 )=0 and |V 1 |=|V 2 |, if |V |≡0(mod 4)), and it can be found in polynomial time. Our techniques can be extended, with similar results, to the case in which the weights are arbitrary (not necessarily ±1), and to the case that p(V ) =0 and the excess supply/demand should be split evenly. They also apply to the problem of partitioning a graph with two types of nodes into two large connected subgraphs that preserve approximately the proportion of the two types.Clearly, the minimum possible value for |p(V 1 )|+|p(V 2 )| that we can hope for is 0, which occurs iff p(V 1 )=p(V 2 )=0. It is easy to show that the problem of determining whether there exists such a 'perfect' partition (and hence the BCPI problem) is strongly NP-hard. The proof is very similar 1. V 1 ∩V 2 =∅ and V 1 ∪V 2 =V ,

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Depth-bounded Graph Partitioning Algorithm and Dual Clocking Method for Realization of Superconducting SFQ Circuits

Pasandi

Pedram

2020

J. Emerg. Technol. Comput. Syst.

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Superconducting Single Flux Quantum (SFQ) logic with switching delay of 1ps and switching energy of 10 −19 J is a potential emerging candidate for replacing Complementary Metal Oxide Semiconductor (CMOS) to achieve very high speed and ultra energy efficiency. Conventional SFQ circuits need Full Path Balancing (FPB), which tends to require insertion of many path balancing buffers (D-Flip-Flops). FPB method increases total power consumption as well as total area of the chip. This article presents a novel scheme for realization of superconducting SFQ circuits by introducing a new depth-bounded graph partitioning algorithm in combination with a dual clocking method (slow and fast clock pulses) that minimizes the aforesaid path balancing overheads. Experimental results show that the proposed solution reduces total number of path balancing buffers and total static power consumption by an average of 2.68× and 60%, respectively, when compared to the best of other methods for realizing SFQ circuits. However, our scheme degrades the peak throughput; therefore, it is especially valuable when the actual throughput of the SFQ circuit is much lower than the peak theoretical throughput. This is typically the case due to high-level data dependencies of the application that feeds data into an SFQ circuit.

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Doubly Balanced Connected Graph Partitioning

Cited by 3 publications

References 17 publications

Mixed-integer programming techniques for the connected max-k-cut problem

Mixed-integer programming techniques for the connected max-k-cut problem

Doubly Balanced Connected Graph Partitioning

Depth-bounded Graph Partitioning Algorithm and Dual Clocking Method for Realization of Superconducting SFQ Circuits

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