M. R. Gary and D. S. Johnson. Computers and Intractability. Freeman, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a spanning tree of any graph is connected. Also note that it is bipartite [10] Let the degree of a spanning tree be the maximum degree of its vertices. The challenge is then to construct a spanning tree with degree less than or equal to 7, if one exists; deciding this is an NP hard problem [7]. It follows that deciding whether connectivity is feasible and constructing a connected logical topology graph which satisfies the desired The degree of a vertex is the number of edges originating from the vertex. A bipartite graph is one where the vertex set can be partitioned in two sets ....

M. R. Gary and D. S. Johnson. Computers and Intractability. Freeman, 1979.

....may, on the basis of test case priority, run as many tests as possible. The possible advantage of prioritization is that its time complexity, O(n 2 ) for the worst case, is better than that for test set size minimization, which is equivalent to the NPcomplete minimal set covering problem [7] and may re Block minimized T MB = Tests that do not execute the modifications T T = Tests that execute the modifications T T P has the same tests as T but in different order. T T MB T is the original regression test set which contains every test in the circle. Figure 2. ....

M. R. Gary and D. S. Johnson, "Computers and Intractability, " Freeman, New York, 1979.

....subschemas tends to minimize the number of relationships between different subschemas. Unfortunately, the problem of partitioning a schema according to the above or similar criteria is NPcomplete, that is, no efficient algorithm is known for it, and it is conjectured that no such algorithm exists [15]. A possible line of action is to combine informational thinning and partitioning, by trying to partition the hierarchical subschema and then use this partition to impose a partition on the original schema. Obviously, this partitioning problem is much simpler than the original problem since the ....

M.R. Gary and D.S. Johnson. Computers and Intractability. Freeman, New York, 1979.

....of IS A links. One would think that the extensive literature on graph partitioning [1, 2, 3, 17] would supply the theoretical means for achieving the kind of partitioning described above. Unfortunately, this expectation fails for two reasons: 1) Partitioning problems tend to be NP complete [12], i.e. probably not solvable by polynomial algorithms; 2) The requirement of meaningful groups is beyond the scope of graph algorithms. To overcome these problems, we have previously combined human expert judgment with algorithmic tools. We have introduced a technique called disciplined ....

Gary, M. R., Johnson, D. S.: Computers and Intractability. Freeman, New York (1979)

....to a forest structure. We formally prove that our approach always finds a forest partition as long as the rules of disciplined modeling are adhered to. Let us note that partitioning networks (graphs) according to various criteria has been shown to be NP complete, i.e. computationally intractable [12]. In previous work [28] we have employed a similar paradigm to reduce the complexity of large object oriented database (OODB) subclass hierarchies. In this paper, we rework and adapt the approach to the IS A hierarchy of an extensive, complex vocabulary. Furthermore, we present an interactive ....

....logical units tends to minimize the number of relationships between different units. Unfortunately, the problem of partitioning a network according to the above or similar criteria is NP complete, that is, no efficient algorithm is known for it, and it is conjectured that no such algorithm exists [12]. A possible line of action is to combine informational thinning and partitioning. After an IS A hierarchy is obtained by applying informational thinning to the original network, the partitioning technique is put to use by partitioning the IS A hierarchy and then imposing this partition on the ....

M. Gary and D. Johnson. Computers and Intractability. Freeman, New York, 1979.

....(6) if links that do not meet the link constraint are removed from the network topology. Hence they are also polynomial time solvable. Finally, problem (7) the Steiner tree problem) and problems (9) 11) and (12) the constrained Steiner tree problems) have been proved to be NP complete in [8]. Table 1 gives a summary of these problems. 3 Multicast Routing Algorithms In this section, we summarize several multicast routing algorithms that can be used to solve the problems classified in Section 2.2. A taxonomy of these multicast routing algorithms is given in Table 2. 1) Shortest ....

M. R. Carey and D. S. Johnson. Computers and intractability. W. H. Freeman Co. New York, 1979.

....constructive proofs can be found for theorems in other areas of graph theory. We begin with some useful definitions. The terminology and notation required for our proofs will be given in the next section. A good reference for any undefined terms in graph theory is [5] and in complexity theory is [8]. We consider only finite undirected graphs without loops or multiple edges. Let G be such a graph with vertex set V (G) and edge set E(G) Then G is hamiltonian if it has a Hamilton cycle, i.e. a cycle containing all of its vertices. We use #(G) for the vertex connectivity of G, #(G) for the ....

M.R.GareyandD.S.Johnson.Computers and Intractability. Freeman, San Francisco, CA, 1979.

....also applies to test sets of 55 , 60 , 65 , 70 and 75 block coverage. the original test set. Hereafter, test set minimization with respect to the number of test cases, is referred to as minimization. Test set size minimization is equivalent to the NP complete minimal set covering problem [4]. A tool called ATAC [6] was used to find minimized test sets. ATAC uses an implicit enumeration algorithm with reductions to find optimal set covering. The technique used in ATAC finds exact solutions for minimizations of all tests examined. Although this technique is exponential on some set ....

M. R. Gary and D. S. Johnson, "Computers and Intractability," Freeman, New York, 1979.

....the same coverage as the entire test set. We define the test set size reduction in terms of number of test cases as j T j Gamma j Tm j j T j 100 (1) How does ATACMIN conduct test set minimization Test set size minimization is equivalent to the NP complete minimal set covering problem [6]. The implicit enumeration technique used in ATACMIN found exact solutions for minimizations of all test sets examined. Although this technique is exponential on some set covering problems derived from Steiner triples [5] no problem derived from test set minimization has been appreciably more ....

M. R. Gary and D. S. Johnson, "Computers and Intractability," Freeman, New York, 1979.

....R i , the interval [n] is partitioned into q intervals. In [10] an algorithm is given to computes an optimal semi generalized block distribution in time O(pqm(m Gamma p) n Gamma q) If, instead of jV1 j = jV2 j = K, we have the restriction jV1 j jV2 j = K then the BCBS problem is in P [5], by reduction to matching. We note that the corresponding problem for the generalized block distribution is of no immediate practical interest. This is because the number of processors p Theta q usually is fixed. Thus the more relevant question is if given the number of processors r, is it ....

M. R. Garey and D. S. Johnson, Computers and Intractability, Freeman, 1979.

....Ave, Murray Hill, NJ 07974. E mail: mihalis research.att.com 1 Introduction Given a finite set of strings, we would like to find their shortest common superstring. That is, we want the shortest possible string s such that every string in the set is a substring of s. The question is NP hard [5, 6]. Due to its important applications in data compression [14] and DNA sequencing [8, 9, 13] efficient approximation algorithms for this problem are indispensable. We give an example from the DNA sequencing practice. A DNA molecule can be represented as a character string over the set of ....

M. Garey and D. Johnson. Computers and Intractability. Freeman, New York, 1979.

....are accepted by the target automaton, and then hypothesize an automaton that is consistent with the data seen so far. If the hypothesized automaton 1 It is generally thought that P F NaN 6= NP , but this is one of the great unproven conjectures of computer science. For more information, see [GJ79] 6 is functionally identical to the target, then the oracle informs the learner that it is done. Otherwise, the oracle presents a counterexample : a string that is accepted by the target automaton and rejected by the hypothesized one, or that is rejected by the target and accepted by the ....

M. Gary and D. Johnson. Computers and Intractability. W. H. Freemand, New York, 1979.

....find a schedule to minimize P i w i f i , where f i = s i t i is the finish time of operation i and s i is its start time. The general problem in which every node has a weight has been shown to be NP hard even for m = 1 provided we permit arbitrary precedence constraints on the operations [9, 15]. The problem is polynomially solvable when the precedence graph is a forest [12] or a generalized seriesparallel graph [1, 15] For m 1, the problem is NP hard even without precedence constraints, unless the weights are all identical in which case it is polynomially solvable; on the other hand, ....

M.R. Garey and D.S. Johnson. Computers and Intractability. W.H. Freeman, San Francisco (1979).

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M. R. Gary and D. S. Johnson. Computers and Intractability. Freeman, 1979.

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M. R. Gary and D. S. Johnson. Computers and Intractability. Freeman, New York, 1979.

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M. R. Gary and D. S. Johnson. Computers and Intractability. Freeman, 1979.

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M. R. Gary and D. S. Johnson. Computers and Intractability. Freeman, NY, 1979.

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Gary M., and Johnson D., Computers and Intractability, W.H. Freeman, New York, 1979.

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Gary M.R. and Johnson D.S. (1979) Computers and Intractability. Published by W.H. Freeman and Company, page 246, 1979.

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Garey, M. R., and Johnson, S. D. (1979). Computers and Intractability, A Guide to the Theory of NP-Completeness, W.H. Freeman & Co.: New York.

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