| M. R. Garey and D.S. Johnson. Computers and Intractibility: A Guide to the Theory of NPcompleteness. W.H. Freeman, San Francisco, 1979. |
....x jl is 1 only when the instruction I kj starts in step l of the schedule. Then, the scheduling can be formulated as a set of equations (from (1) to (5) that have to be satisfied. The first four equations are the resource constrained minimum latency scheduling equations and described in detail in [38]. Briefly, equation (1) tells us that the start time of each instruction is unique and equation (2) shows us that the dependency relations in G Dk must be satisfied. The resource constraint must be satisfied at every cycle. An instruction I kj is executing at cycle l when x jm mld = 1. ....
...., 01 12 1 l (5) xxl iq q l i jq l j = 01 1 : master instruction q=1 shadow instruction 4. 2# List Scheduling The disadvantage of the integer linear programming formulation is the computational complexity of the problem: generally it is an NP complete problem [38]. The number of variables, the number of inequalities and their tightness affect the ability of computer programs to find a solution. Heuristic algorithms have been developed to solve this intractable problem. We consider the list scheduling algorithm [39] to schedule master and shadow ....
Garey, M. R. and D. S. Johnson, Computers and Intractibility: a Guide to the Theory of NP-Completeness, New York: W. H. Freeman and Company, 1979.
....requests is proportional to the token circulation time. Hence, the token circulation path should be chosen to minimize the token circulation time. The problem of selecting an optimal token circulation route is identical to the well known traveling salesman problem, which is known to be NP complete [12]. For small enough domains, the traveling salesman problem can be solved by brute force. For larger domains, however, a heuristic may be necessary to achieve a near optimal circulation path. There are many such heuristics like the nearest neighbor approximation and Christofides 1 2approximation ....
M.R. Garey and D.S. Johnson, Computers and Intractibility: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, San Fransico, 1979.
....unit for register . Note that the cardinality of is at most but can be less since multiple registers in can send data to the same execution unit in . Hence, We next prove that finding the level MFVS is a computationally intractable problem. We start by posing the problem in the standard form [51] for studying its computational complexity. PROBLEM: level feedback vertex set. INSTANCE: Directed graph , positive integer , positive integer . QUESTION: Is there a subset with such that contains vertices which make every directed cycle in level observable and level controllable. We present ....
M. Garey and D. Johnson, Computers and Intractibility: A Guide to the Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
....P S . In case of a shared OBDD representation, the equivalence test itself consists of a single pointer comparison. Each step of symbolic simulation can be performed eciently with respect to the OBDD sizes of the predecessor gates. This shows that the diculty of the NP complete equivalent test [20] has now been shifted into the representation size. Unfortunately, since each synthesis step can potentially produce an OBDD that is the product of its argument sizes, the OBDD representation of either C or S can be of exponential size. If C and S are not equivalent, the operation PC P S gives ....
M. R. Garey, D. Johnson, "Computers and Intractibility: A Guide to the Theory of NP-Completeness", W. H. Freeman, 1978.
....do so, we construct Spiral Galaxies puzzles which correspond to arbitrary Boolean circuits. A circuit will be satisfied, that is, have a set of inputs which give the desired outputs) if and only if the corresponding puzzle has a solution. Since Satisfiability is the canonical NP complete problem [4], this will show that Spiral Galaxies puzzles are NP hard. We complete the proof by showing that a solution to a Spiral Galaxies puzzle can be checked in polynomial time. Similar approaches to proving puzzles are NP complete are taken in [1 3, 5 10] To build a circuit, we first need wires capable ....
M.R. Garey and D.S. Johnson, Computers and Intractibility: A Guide to the Theory of NP-Completeness. W.H. Freeman, 1979.
....open squares. In [4] the authors prove that Push k is NP hard using a reduction from the 3 coloring of planar graphs. That is, for a given planar graph, they build a Push k puzzle that can be solved if and only if the vertices of the original graph can be 3 colored. As 3 colorability is NP hard [9], so is Push k. Their construction depends on the existence of four gadgets: a One Way gadget that can only passed in one direction, a Fork gadget that allows only one of several exits to be used, an XOR Crossing gadget which allows possible passageways to cross provided that only one of these is ....
M.R. Garey and D.S. Johnson, Computers and Intractibility: A Guide to the Theory of NP-Completeness. W.H. Freeman, 1979.
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M. R. Garey and D.S. Johnson. Computers and Intractibility: A Guide to the Theory of NPcompleteness. W.H. Freeman, San Francisco, 1979.
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GAREY,M.R.AND JOHNSON, D. S. 1979. Computers and Intractibility -- A Guide to the Theory of NP-Completeness. W. H. Freeman and Co., New York, NY.
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M. R. Garey and D. S. Johnson. Computers and Intractibility: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, San Fransisco, 1979.
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M.R. Garey and D.S. Johnson, Computers and Intractibility: A Guide to the Theory of NP-Completeness, Freeman, New York, 1979.
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M. Garey and D. Johnson. Computers and Intractibility: A Guide to the Theory of NP-Completeness. W.H. Freeman Company, 1979.
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Garey, M.R., Johnson, D.S.: Computers and Intractibility: A guide to the theory of NP-completeness. W. H. Freeman (1979)
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M.R. Garey and D.S. Johnson. Computers and Intractibility - A guide to the theory of NP-completeness. W.H. Freeman and Company, 1979.
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M. Garey and D.S. Johnson, Computers and Intractibility: A Guide to the Theory of NPCompleteness (Freeman [1979])
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M. R. Garey and D. S. Johnson, Computers and intractibility: A Guide to the theory of NP-completeness,W.H.Freeman, San Francisco, 1979.
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M. R. Garey and D. S. Johnson, Computers and Intractibility: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, 1979.
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M. Garey and D. Johnson. Computers and Intractibility: a Guide to the Theory of NP-Completeness. Freeman, 1979. 14
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M. Garey and D. Johnson, Computers and Intractibility: A Guide to the Theory of NPCompleteness. W.H. Freeman and Company, 2000.
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M.R. Garey and D.S. Johnson, Computers and Intractibility: A Guide to the Theory of NPCompleteness, Freeman, New York, 1979.
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M. Garey and D. Johnson. "Computers and Intractibility: A Guide to the Theory of NP-Completeness.". W.H. Freeman, New York, 1979.
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M. Garey and D. Johnson. Computers and Intractibility: A Guide to the Theory of NPCompleteness. Freemans, San Francisco, 1979. 29
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M. R. Garey and D. S. Johnson. Computers and Intractibility: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York, 1979.
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M. R. Garey and D. S. Johnson. Computers and Intractibility: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York, 1979.
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M. Garey and D. Johnson. Computers and Intractibility: A Guide to the Theory of NPCompleteness. Freemans, San Francisco, 1979.
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M. R. Garey and D. S. Johnson. Computers and Intractibility: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York, 1979.
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