D.S. Johnson, "The NP -completeness column: an ongoing guide", J. Algorithms 6 (1985) pp. 434-451.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....graph, then S(G) 2. Proof : A graph is subhamiltonian if it is a subgraph of a planar graph that has a hamiltonian cycle. Bernhart and Kainen [1] prove that if G is a subhamiltonian graph, then S(G) 2. Clearly every Halin graph is planar. Furthermore, every Halin graph has a hamiltonian cycle [5]. Thus, every Halin graph G is subhamiltonian and therefore has S(G) 2. There exist Halin graphs that require 2 stacks. For example, K 4 is a Halin graph and requires 2 stacks, since S(K n ) bn=2c. Therefore, 2 stacks are necessary and sufficient for the class of Halin graphs. 3 Queue Layouts ....

D. S. Johnson. The NP-completeness column: An ongoing guide. JournalofAlgorithms, 6:434--451, 1985.

....language (L, is in the average case version of P, average P, if there is an algorithm deciding membership for L in time polynomial on average a concept to be discussed formally later in this paper. There is a vast literature on ACTC; for more information, we recommend the overviews surveys [Johnson, 1984; Gurevich, 1989; 1991a; 1991b; Impagliazzo, 1995; Wang, 1997; Goldreich, 1997] as starting points. Average case compilability. In laying down a theory for average case compilability, we want to soften the definition of formalism A is compilable to formalism B by relaxing the requirement that ....

David Johnson. The NP-completeness column: an ongoing guide. Journal of Algorithms, 5:284-299, 1984.

....them. The graph isomorphism problem is therefore to decide whether two graphs are isomorphic and, in the affirmative, to find an isomorphism. The graph isomorphism problem is one of those few combinatorial optimization problems which still resist any computational complexity characterization [19, 28]. Despite decades of ac tive research, no polynomial time algorithm for it has yet been found. At the same time, while clearly belonging to NP, no proof has been provided that it is NP complete. Indeed, there is strong evidence that this cannot be the case, for otherwise the polynomial hierarchy ....

JOHNSON, D. S.: 'The NP-completeness column: An ongoing guide', J. Algorithms 9 (1988), 426-444.

....general graphs. We conjecture that the formal complexity of the problem is significantly reduced for planar graphs. There may be a (pseudo)polynomial time algorithm in this case. For example, a number of network partitioning problems are easier for planar graphs than they are for general graphs [6]. ....

D. Johnson. The np-completeness column: an ongoing guide (16th). Journal of Algorithms, 6(3):434-- 451, 1985.

....of computation. Nevertheless, theoretical results identify a sub class of NP complete problems for which a reasonable approximation scheme can produce high quality results in polynomial time. A standard theoretical metric for the quality of an approximation algorithm is its worst case ratio [Johnson, 1992] The nearness to optimality of a given solution can be expressed as a ratio of its value to that of an optimal solution. The worst case ratio for an approximation algorithm indicates just how far from 1 that ratio can be for a solution it generates. It is normally assumed that the numerator of ....

.... problem, for example, then guaranteeing a worst case ratio of for any constant is just as hard as finding an optimal solution [Sahni and Gonzalez, 1976] More recently, additional results regarding approximation algorithms were derived based on their connection to multiple provers [Johnson, 1992] An interesting question to ask is what is the best possible ratio that can be guaranteed for a particular NP complete problem in polynomial time, assuming that . There are two possible answers to this question. Either there is an approximation threshold such that no polynomial time ....

D. S. Johnson. The NP-completeness column: An ongoing guide. To appear in J. Algorithms, 1993.

....that CWA(T ) is consistent i the intersection of all Herbrand models of T is a model of T . Hence clearly, Lemma 3.5 CWA(T ) is consistent i T has a unique minimal model M and CWA(T ) is logically equivalent to M . CWA consistency checking turns out to be the unique solution variant (cf. [14] for uniqueness questions) of the following problem MINSAT: Has T a minimal model Note that the latter is simply the NP complete SATISFIABILITY (SAT) problem, since every consistent theory has a minimal model. The uniqueness variant UMINSAT is to decide if T has exactly one minimal model. Note ....

D. S. Johnson. The NP-Completeness Column { An Ongoing Guide. Journal of Algorithms, 6(2):291-305, 1985. Column 15: Uniqueness.

....graphs avoiding a given fixed graph as a minor, which was developed by Robertson and Seymour in their fundamental 7 Q4, 2 Fig. 3. Fig. 4. series of papers concerning graph minors (see [40 47] This structure theory has many applications in combinatorics, complexity theory and logic (see, e.g. [31, 39, 41, 49, 62]) Here the following part of it will be used. Definition. A tree decomposition of a graph G is a pair (T, X) where T is a tree and X= X:te V(T) is a family of subsets of V(G) with the following properties: i) I.J (X, t v(r) V(G) ii) for every edge e of G there exists t V(T) such ....

D.S. Johnson, The NP-completeness column: an ongoing guide, J. Algorithms 6 (1987).

....may be amenable to polynomial solution of optimization problems which are in general NP hard, e.g. minimum coloring or maximum independent set. For a systematic study of such families of graphs, their properties, their recognition and many fascinating applications see [17, 29] References [24] and [3] review many additional results. In practice, it may happen that the input graph may not belong to the desired family but is close to the family in some sense, so one may wish to slightly relax the condition for accepting a given input. The type of relaxation depends on the application. ....

D. S. Johnson. The NP-completeness column: an ongoing guide. J. of Algorithms, 6:434--451, 1985.

....computational aspects of VLSI design are studied in the book [ULLM84] David Johnson s ongoing column The NP Completeness Column in the Journal of Algorithms, Academic Press, is a good source for current research on NP completeness. In fact, the Dec. 1982 column is devoted to routing problems, [JOHN82]. 2. SOME DESIGN AUTOMATION PROBLEMS There are numerous steps in the process of designing complex digital hardware. It is generally recognized that the following classes of design activities occur: 1) System design. This is a very high level architectural design of the system. It also defines ....

Johnson, D., "The NP-Completeness Column: An ongoing guide", Jr of Algorithms, Dec 1982, Vol 3, No 4, pp. 381395.

....is a propositional formula whose atoms are sign conditions on polynomials built from the IXlj. We can also replace the relation 4 by an objective function and ask for its extremal value: maxo(x . x) F(IXll . IXzIm) Problems in these classes will be called EMS problems. M. O. Rabin in [29] introduced a notion of model interpretability of theories as a useful tool to prove decidability or undecidability of given theories. An extended variant of interpretability was used by Compton and Henson [17] to investigate the complexity of logical theories. We will introduce a related notion ....

....used method in mathematical logic to transform one theory into another one. Especially the method of syntactic interpretation was used by Tarski, Mostowski, and Robinson [41] to deduce decidability or undecidability of theories from other theories. Semantic interpretations were used by Rabin [29] as a variant of the interpretability concept and proved to be a useful tool to show decidability or undecidability of theories (see also [30] A different variant was introduced by Compton and Henson [17] to prove lower bounds on the complexity of logical theories. The notion of interpretability ....

D. S. JOHNSON, The NP-completeness column: An ongoing guide, J. Algorithms 8 (1987), 285-303.

....many classes of graphs whose structure is so closely related to trees, that one can use this fact to solve problems for them whose solutions are unknown or difficult for arbitrary graphs. A highlight in this research is the fundamental series of papers of Robertson and Seymour (see, e.g. Johnson [28] for a survey) on graph minors. Robertson and Seymour introduced in [31] the notion of treewidth of a graph. Intuitively, a graph of treewidth w can be expressed as the (nondisjoint) union of graphs of size v I arranged as nodes in a tree in such a way that the set of nodes containing a given ....

....of the tree. The treewidth is thus a parameter that measures how close to a tree a graph is. Its exact definition will be given in Section 3. The concept of treewidth and similar concepts found deep applications in the design of (at least theoretically) efficient algorithms (see, e.g. Johnson [28]) Many important classes of graphs have a universal bound for the treewidth of their members. As an example, trees and forests have treewidth 1, series parallel graphs and outerplanar graphs 2, almost trees with k additional edges have treewidth k 1, Halin graphs g 3, and members of ....

D. S. JOHNSON, The NP-completeness column: An ongoing guide, J. Algorithms 6 (1984), 434-451.

....of a dominating set in G. A dominating set G in G is minimum if D = #(G) For a set X V (G) we say that X dominates N [X] Let be a set of graphs. A graph G is called Z free if G does not contain any graph of as an induced subgraph. It is well known (see Bertossi [1] Johnson [3], and Korobitsin [4] that the problem of finding a minimum dominating set is NP complete for both P 5 free graphs and K p free graphs (p 3) We prove that this problem can be solved in polynomial time for (K p , P 5 ) free graphs. Definition 1 For n m 1 we define a graph H = S(n, m) as ....

D. S. Johnson, The NP-completeness column: an ongoing guide, J. Algorithms 5 (1984) 147--160

....Since the formula is the main key to solving the FSP problem, our work has the merit of giving a direct and elegant proof for this formula. It is also interesting to note that the more general version of the FSP problem, where degenerated rectangles are allowed, was believed to be NP hard [Joh82, Lin82] Only recently, nearly ten years after the publication of the erroneous NPhardness proof in [Lin82] a polynomial time algorithm has been discovered in [SG92] giving a surprising solution to this problem. Essentially, the correctness of the algorithm in [SG92, SG93] is based on a formula ....

D. S. Johnson. The NP-completeness column: an ongoing guide. J. Algorithms, 3:182--195, 1982.

....away finally arrives. V. SOLVING MAx SATISFIABILITY A. Introduction The classifical definition of max satisfiability involves finding a satisfying assignment for clauses in a Boolean function, where the clauses represent disjunctions of literals [5] Algorithms have been proposed (e.g. [8]) for exact and approximate solutions to this problem. Here, we are concerned with finding satisfying assignments for arbitrary Boolean functions that can themselves involve conjunctive and disjunctive terms. In the sequel, we present two strategies we have developed for solving general ....

D. S. Johnson, "The NP-completeness column: An ongoing guide," J. Algorithms, vol. 6, pp. 291-305, 1985.

....furthest away finMly arrives. 5 Solving Max Satisfiability 5. 1 Introduction The classical definition of max satisfiability involves finding a satisfying assignment for clauses in a Boolean function, where the clauses represent disjunctions of literals [2] Algorithms have been proposed (e.g. [5]) for exact and approximate solutions to this problem. tiere, we are concerned with finding satisfying assignments for arbitrary Boolean functions that can themselves involve conjunctive and disjunctive terms. In the sequel, we will present two strategies we have developed for general ....

D. S. Johnson. The np-completeness column: an ongoing guide. Jottrnal of Algorithms, 6:291-305, 1985.

....to be NP complete, when restricted to cogr phs (and even complete graphs) even when all weight are either 1 or 2. 1 Introduction As it is generally believed that NP complete problems are not solvable in polynomial time, much research has been done on the complexity of NPcomplete problems. In [4] an overview is given of the known complexity of some well known NP complete problems when restricted to a number of important classes of grapks. It appears that some clases will uually render a problem to be solvable in polynomial time (e.g. the classes of trees, partial k trees, or interval ....

D. S. Johnson. The NP-completeness column: an ongoing guide. J. of Algorithms, 6:434-451, 1985. 8

.... graphs in general I Introduction Games are not only a popular pastime, but can also serve as a model for several different phenomena, like conflicts between parties with different interests, fault tolerance, worst case complexity of algorithms (see e.g. 6] and complexity theory (see e.g. [5]) In this paper we concentrate on the problem to determine whether there is a winning strategy for the first (or second) player in a given game instance from a certain class of games. We consider the following type of game: The game is played on a given directed or undirected graph. Two players ....

D. Johnson. The NP-completeness column: An ongoing guide. J. Algorithms, 4:397-411, 1983.

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D.S. Johnson, "The NP -completeness column: an ongoing guide", J. Algorithms 6 (1985) pp. 434-451.

No context found.

D. Johnson "The NP-Completeness Column - an Ongoing Guide. Journal of Algorithms, 5:284-299, 1984.

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D.S. Johnson, "The NP-completeness column: an ongoing guide", Journal of Algorithms, vol. 7, pp. 174-184, 1986.

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D.S. Johnson. The NP-completeness column: An ongoing guide. The many faces of polynomial time. Journal of Algorithms, 8:285-303, 1987.

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D. S. Johnson, The NP-completeness column: an ongoing guide, J. Algorithms 8(3) (1987) 438-448.

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D. Johnson, \The NP-Completeness Column: An Ongoing Guide", Journal of Algorithms, Vol.13, 502-524,1992.

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D. S. Johnson, The NP-Completeness Column: An Ongoing Guide, J. Algorithms, 3 (1982), page 184.

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D. S. Johnson, "The NP-Completeness Column: An Ongoing Guide," Journal of Algorithms 1987.

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