A catalog of Hanan grid problems

Zachariasen, Martin

doi:10.1002/net.1026

Cited by 33 publications

(21 citation statements)

References 24 publications

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“…It terminates when only one subtree remains. For efficient implementation, the RSA/G first sorts all the nodes on the Hanan grid [17] in decreasing distance to the source s, and visits each node maintaining a peer set P of subtree roots. Details are in the pseudo code in table 1.…”

Section: K-idea/g Heuristic For Mrsamentioning

confidence: 99%

Low power gated bus synthesis using shortest-path Steiner graph for system-on-chip communications

Wang

Chou

Salefski

et al. 2009

Proceedings of the 46th Annual Design Automation Conference

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Power consumption of system-level on-chip communications is becoming more significant in the overall system-on-chip (SoC) power as technology scales down. In this paper, we propose a low power design technique of gated bus which can greatly reduce power consumption on state-of-the-art bus architectures. By adding demultiplxers and adopting a novel shortest-path Steiner graph, we achieve a flexible tradeoff between large power reduction versus small wirelength increment. According to our experiments, using the gated bus we can reduce on average 93.2% of wire capacitance per transaction, nearly half of bus dynamic power and on a scale of 5%∼10% of total system power.

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Section: K-idea/g Heuristic For Mrsamentioning

confidence: 99%

Low power gated bus synthesis using shortest-path Steiner graph for system-on-chip communications

Wang

Chou

Salefski

et al. 2009

Proceedings of the 46th Annual Design Automation Conference

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show abstract

“…In our reduction, each strip is used to express an assignment of a boolean variable, which is indicated by which side of the strip the path (network) includes. Specifically, by definition of vertical strips, we can assume that the strip path of R(p, q) does not contain any vertical line segment whose x-coordinate is not equal to p.x or q.x [12], thus has only one horizontal line segment (switch segment). For a nice strip path collection E S , there are two ways of connecting p and q using a strip path in E S , which can be used to express the value of a variable v in ψ.…”

Section: Preliminariesmentioning

confidence: 99%

“…Now we show that it is in NP. By [12], there exists a minimum Manhattan network in the Hanan grid of T which contains a polynomial number of edges. Let the network, denoted by G, be a certificate and it can be verified in polynomial-time by computing L(G) and comparing L(G) with a given bound of the network's length.…”

Section: Theorem 3 the Minimum Manhattan Network Problem Is Strongly mentioning

confidence: 99%

Minimum Manhattan Network is NP-Complete

Chin

Guo

Sun

2011

Discrete Comput Geom

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Given a set T of n points in R 2 , a Manhattan network on T is a graph G with the property that for each pair of points in T , G contains a rectilinear path between them of length equal to their distance in the L 1 -metric. The minimum Manhattan network problem is to find a Manhattan network of minimum length, i.e., minimizing the total length of the line segments in the network.In this paper, we prove that the decision version of the MMN problem is strongly NP-complete, using a reduction from the well-known 3-SAT problem, which requires a number of gadgets. The gadgets have similar structures, but play different roles in simulating a 3-CNF formula.

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“…Specifically, from the definition of vertical strip, we can assume that the strip path of R(p, q) would not contain any vertical line segment whose x-coordinate does not equal to p.x or q.x [10],…”

Section: Preliminariesmentioning

confidence: 99%

Minimum Manhattan network is NP-complete

Chin

Guo

Sun

2009

Proceedings of the Twenty-Fifth Annual Symposium on Computational Geometry

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A rectilinear path between two points p, q ∈ R 2 is a path connecting p and q with all its line segments horizontal or vertical segments. Furthermore, a Manhattan path between p and q is a rectilinear path with its length exactly dist(p, q) := |p.x − q.x| + |p.y − q.y|.Given a set T of n points in R 2 , a network G is said to be a Manhattan network on T , if for all p, q ∈ T there exists a Manhattan path between p and q with all its line segments in G. For the given point set T , the Minimum Manhattan Network (MMN) Problem is to find a Manhattan network G on T with the minimum network length.In this paper, we shall prove that the decision version of MMN is strongly N P -complete, using the reduction from the well-known 3-SAT problem, which requires a number of gadgets. The gadgets have similar structures, but play different roles in simulating the 3-SAT formula. The reduction has been implemented with a computer program.

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A catalog of Hanan grid problems

Cited by 33 publications

References 24 publications

Low power gated bus synthesis using shortest-path Steiner graph for system-on-chip communications

Low power gated bus synthesis using shortest-path Steiner graph for system-on-chip communications

Minimum Manhattan Network is NP-Complete

Minimum Manhattan network is NP-complete

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