F. O. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing, 4:221--225, 1975.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....within the bounding region is a variation upon a mazerouting strategy. Maze routing is a standard routing method of connecting two terminals in the presence of obstacles. The problem first appears in the literature in 1961 [42] There have been significant improvements since then. e.g. 57] [29][58] 66] 9] The basic idea behind maze routing is as follows. Mark the source terminal, s. Every point that is directly adjacent from s is marked as distance 1 away. Then every unmarked (b) a) Figure 5.1: Example of re routing inside the bounding box. First, the area to be re routed is ....

F. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM Journal of Computing, 4(3):221--225, September 1975.

....section, we propose four distinct heuristics for feature graph bipartization which are experimentally studied in the next section. The planarity of the feature graph greatly reduces complexity of bipartizing. In fact, edge deletion bipartization can be solved in polynomial time for planar graphs [22, 10]. An efficient implementation of the optimal algorithm for edge deletion bipartization is suggested in [3] On the other hand, node deletion bipartization of planar graphs is NP hard [27] but provably better approximate solutions can be found in planar graphs rather than in general graphs. The ....

F. O. Hadlock, "Finding a Maximum Cut of a Planar Graph in Polynomial Time", SIAM J. Computing 4(3) (1975), pp. 221225.

....Computing both the ground states and the partition function for planar graphs can be done in polynomial time, 1] and [27] Planarity and its duality are fundamental for obtaining computationally tractable solutions. For the minimum weight cuts in planar graphs, algorithms are due to Hadlock 1975 [12] and Goodman and Hedetniemi [11] and [32] The problem of computing the partition function for the zero field Ising model for finite planar lattices is equivalent to that of computing a determinant, and therefore, can be done in polynomial time. For planar graphs, Pfaffian orientations could be ....

F. O. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM J. Computing, 4, 1975.

....Algorithm GreedyCut cubic [123, 155] or quasi planar [14] Since this problem is so hard, researchers have been working along two different directions. The first direction is to look for algorithms for MAXCUT on special graphs. It is known that MAXCUT is polynomial time solvable on planar graphs [72, 114], weakly bipartite graphs [69] and graphs that are not contractible to K 5 [15] The other direction is to look for approximation algorithms. It is known that MAXCUT is MAX SNP complete, even if the degree of the graph is bounded by a constant [116] It follows from [11] that MAXCUT does not ....

F. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing, 4(3):221--225, Sept. 1975.

....by replacing multiple edges connecting a pair of nodes faces f and g with a single edge of minimum weight. If we define T to be the set of odd faces of G, then finding the minimum cost feasible solution is the same as solving the T join Problem for D. The T join problem was reduced by Hadlock [8] and Orlova Dorfman [20] to the Minimum Weight Perfect Matching Problem. Lemma 4.2 The T join problem for a graph with n nodes can be reduced to MinimumWeight Perfect Matching problem in a complete graph with jT j nodes. 12 (f) e) b) c) d) a) Figure 7: From the conflicts between ....

....an instance of T join problem with m edges by applying a perfect matching algorithm to a graph with O(m) edges. In this manner, we obtain an algorithm for the T joint problem that runs in time roughly O(n 3=2 ) see Theorem 5. 6) rather than O(n 3 ) implied by the method known previously [20, 8]. Finally, we refine this idea to improve the size of the resulting instance of perfect matching (and consequently, the overall running time) by a constant factor. 5.1 Opportunistic Reductions In this subsection we describe simplifying, opportunistic reductions that eliminate the nodes of degree ....

F. O. Hadlock, "Finding a Maximum Cut of a Planar Graph in Polynomial Time", SIAM J. Computing 4(3) (1975), pp. 221-225.

....degree of four. Kajitani has shown in [75] that the problem transforms to a maximum cut problem in planar graphs if the maximum junction degree is three, or if vias are not allowed to be placed on junctions. Several polynomial time algorithms based on Hadlock s planar maximum cut algorithm [65], or related methods have been proposed in [75] 24] 130] 134] They all have running time O(n 3 ) where n is the number different wire segment clusters (possibly larger than the number of nets) In [142] the problem is also formulated as a maximum cut problem in planar graphs, but since ....

F. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM J. Comput., 4:221--225, 1975.

.... appears in scientific disciplines ranging from VLSI design [11] to statistical physics, 2, 7] Unfortunately the max cut problem in its general form is well known to be NP complete, 9] There exist several subclasses of graphs, for which the max cut problem is tractable, such as planar graphs [13, 8], or more generally graphs not contractible to K 5 (see [1] The polynomial solvability on these special graphs is related to a complete description of their cut polytopes and does not seem to allow a generalization to wider classes of graphs. Computational experiments based on polyhedral ....

F. O. HADLOCK. Finding a maximum cut of a planar graph in polynomial time. SIAM J. Comput. 4, (1975) 221--225.

....of wire remain on the same level. The problem is modeled with a simple undirected graph and reduced to the problem of finding the max cut of a contraction of this graph. The latter happens to be a planar graph, and there are polynomial time algorithms for the max cut problem on planar graphs [Had75,OD72]. However, a slight complication of the problem yields contracted graphs with the property that for any vertex v, G Gamma v is planar. The max cut problem remains NP hard for such cases. 2 Previous Work The history of work on approximate graph bisection problems dates back at least thirty years. ....

F.O. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM Journal of Computing, 4:221--225, 1975.

....especially for planar graphs. The feedback problem in general undirected graphs is trivially the complement of the maximum spanning tree problem. The minimum weight bipartization problem is complementary to the maximum weight cut problem in planar graphs, which is polynomial time solvable (Hadlock [18]; Orlova and Dorfmann [24] since the problem is equivalent to a T join problem in the dual graph. The feedback arc set problem in planar digraphs is well known to be reducible to finding a minimum weight dijoin in the dual graph, which can be solved in polynomial time (see, for example, ....

F. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing, 4:221--225, 1975.

.... is one of the Karp s original NP complete problems [37] and has long been known to be NP complete even if the problem is unweighted; that is, if w ij = 1 for all (i; j) 2 E [19] The MAX CUT problem is solvable in polynomial time for some special classes of graphs (e.g. if the graph is planar [52, 27]) Besides its theoretical importance, the MAX CUT problem has applications in circuit layout design and statistical physics (Barahona et al. 4] For a comprehensive survey of the MAX CUT problem, the reader is referred to Poljak and Tuza [62] Because it is unlikely that there exist efficient ....

F. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing, 4:221--225, 1975.

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F. O. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing, 4:221--225, 1975.

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F. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing, 4:221--225, 1975.

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F. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM J. Comput., 4(3):221--225, 1975.

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F. Hadlock, Finding a Maximum Cut of a Planar Graph in Polynomial Time, SIAM Journal on Computing 4 (1975), pp. 221-225.

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F. O. Hadlock, Finding a Maximum Cut of a Planar Graph in Polynomial Time, SIAM J. Computing 4 (1975), 221-225.

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F. O. Hadlock, Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing 4(3), 221-225, 1975

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F. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing, 4:221--225, 1975.

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F. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing 4(1975), pp. 221-225.

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F. O. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM J. Comput., 4:221-225, 1975.

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F. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing, 4:221--225, 1975.

No context found.

F. Hadlock. Finding a maximum cut of planar graph in polynomial time. SIAM J. Comput., 4:221--225, 1975.

No context found.

F. Hadlock, Finding a Maximum Cut of a Planar Graph in Polynomial Time, SIAM Journal on Computing 4 (1975), pp. 221-225.

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F. HADLOCK. Finding a maximum cut of a planar graph in polynomial time. SIAM J. Comput., 4(3):221--225, 1975.

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F.O. Hadlock, Finding a Maximum Cut in a Planar Graph in Polynomial Time, SIAM Journal on Computing, No. 4, 1975, pp. 221-225.

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F. O. HADLOCK, Finding a Maximum Cut of a Planar Graph in Polynomial Time, SIAM J. Computing, 4 (1975), pp. 221--225.

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