M. Marathe, H. Hunt III and S. Ravi, The complexity of approximating PSPACE-complete problems for hierarchical specifications, Nordic Journal of Computing 1 (1994) 275--316.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....An early example of a nonapproximability result is Orlin s [20] paper on approximating a periodic version of the Knapsack problem. Periodic and hierarchically defined structures have then been studied quite extensively since such problems arise in scheduling and VLSI applications. Marathe et al. [19] contains several results of this type. Nonapproximability results for some other problems, including Max QDones and Finite Function Generation, can be found in Hunt et al. 16] and Jonsson [17] The techniques of probabilistically checkable proofs which have been so important in understanding ....

M. Marathe, H. Hunt III and S. Ravi, The complexity of approximating PSPACE-complete problems for hierarchical specifications, Nordic Journal of Computing 1 (1994) 275--316.

....Hill, NJ 07974 0636 (lund research.att.com) AT T Laboratories, Room 2D149, 600 Mountain Avenue, Murray Hill, NJ 07974 0636 (shor research.att.com) 370 A. CONDON, J. FEIGENBAUM, C. LUND, AND P. SHOR of periodic structures, arise in many VLSI and scheduling applications (see, for example, [18] for references to these and other applications) Because such representations can implicitly describe a structure of exponential size, using just polynomial space, the associated problems are often PSPACE hard. As early as 1981, Orlin [20] claimed a negative result on approximating a PSPACE hard ....

....on approximating a PSPACE hard periodic version of the Knapsack problem, namely that a fully polynomial approximation scheme exists for this problem only if NP = P. Orlin did not address whether in fact it might be PSPACE hard to approximate this function. On the positive side, Marathe et al. [18] recently developed constant factor approximation algorithms for PSPACE hard problems, including the Max Cut and Vertex Cover problems for certain restricted classes of hierarchically represented graphs. In related work, Marathe et al. 19] applied results of Arora et al. 2] to show that these ....

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M. Marathe, H. Hunt III, and S. Ravi, The complexity of approximating PSPACE-complete problems for hierarchical specifications, Nordic J. Comput., 1 (1994), pp. 275--316.

....specification of a graph may be logarithmic in the size of the graph. Partly as a result of this, optimization functions defined on hierarchical structures are often PSPACE hard, motivating the study of approximation algorithms for optimization functions on such succinct structures. Marathe et al. [17] described polynomial time approximation algorithms for hierarchical versions of the MAX CUT and SAT problems, both of which have a performance guarantee of 1=2. This is not as good as the best performance guarantees for the non hierarchical versions of these problems. One goal of our work is to ....

.... of approximation results for several other PSPACE hard problems (but not for hierarchically defined problems) based on reductions from debate systems can be found in [4, 5] A hardness of approximability result for a PSPACE hard hierarchically defined linear programming problem can be found in [17]. Our second result is that there is an efficient approximation algorithm for the H MAX SAT problem with performance guarantee 2 3. Specifically, given any H CNF formula F , our algorithm efficiently produces a hierarchical specification of a truth assignment to the variables of E(F ) that is ....

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M. Marathe, H. Hunt III, and S. Ravi, The Complexity of Approximating PSPACE-Complete Problems for Hierarchical Specifications, Proc. 20th International Colloquium on Automata, Languages, and Programming, 1993, pp. 76--87.

....have such algorithms if and only if PSPACE = P. One interesting class of results concern problems on hierarchically defined structures, such as graphs. Problems on these structures, and on a related class of periodic structures, arise in many VLSI and scheduling applications (see, for example, [18] for references to these and other applications) Because such representations can implicitly describe a structure of exponential size, using just polynomial space, These results first appeared in our Technical Memorandum [11] They were presented in preliminary form at the 9th Annual IEEE ....

....on approximating a PSPACE hard periodic version of the Knapsack problem, namely that a fully polynomial approximation scheme exists for this problem only if NP = P. Orlin did not address whether in fact it might be PSPACE hard to approximate this function. On the positive side, Marathe et al. [18] recently developed constant factor approximation algorithms for PSPACE hard problems, including the Max Cut and Vertex Cover problems for certain restricted classes of hierarchically represented graphs. In related work, Marathe et al. 19] applied results of Arora et al. 2] to show that these ....

[Article contains additional citation context not shown here]

M. Marathe, H. Hunt III, and S. Ravi, The Complexity of Approximating PSPACEComplete Problems for Hierarchical Specifications, Proc. 20th International Colloquium On Automata, Languages and Programming, A. Lingas, R. Karlsson, and S. Carlsson (eds.), Lecture Notes in Comput. Sci., vol. 700, Spinger, Berlin, 1993, pp. 76-87.

....have such algorithms if and only if PSPACE = P. One interesting class of results concern problems on hierarchically defined structures, such as graphs. Problems on these structures, and on a related class of periodic structures, arise in many VLSI and scheduling applications (see, for example, [18] for references to these and other applications) Because such representations can implicitly describe a structure of exponential size, using just polynomial space, the associated problems are often PSPACE hard. As early as 1981, Orlin [20] claimed a negative result on approximating a PSPACE hard ....

....on approximating a PSPACE hard periodic version of the Knapsack problem, namely that a fully polynomial approximation scheme exists for this problem only if NP = P. Orlin did not address whether in fact it might be PSPACE hard to approximate this function. On the positive side, Marathe et al. [18] recently developed constant factor approximation algorithms for PSPACE hard problems, including the Max Cut and Vertex Cover problems for certain restricted classes of hierarchically represented graphs. In related work, Marathe et al. 19] applied results of Arora et al. 2] to show that these ....

[Article contains additional citation context not shown here]

M. Marathe, H. Hunt III, and S. Ravi, The Complexity of Approximating PSPACEComplete Problems for Hierarchical Specifications, Proc. 20th International Colloquium On Automata, Languages and Programming, A. Lingas, R. Karlsson, and S. Carlsson (eds.), Lecture Notes in Comput. Sci., vol. 700, Spinger, Berlin, 1993, pp. 76-87.

....Before discussing our algorithms, it is important to understand what we mean by a polynomial time approximation algorithm for a problem Pi, when the instance is specified succinctly. Our definition of approximation algorithm is best understood by means of the following example from [MHR93]. 6 We remark that most of the problems solvable in polynomial time for consistent specifications [BOW83] are solvable in polynomial time for k near consistent specifications (for any fixed k 0) Example: Consider the minimum vertex cover problem, where the input is a succinct specification of ....

M.V. Marathe H.B. Hunt III and S.S. Ravi, "The Complexity of Approximating PSPACE-Complete Problems for Hierarchical Specifications ", in the proceedings of ICALP'93, 1993, pp 76-87.

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M. V. Marathe, H. B. Hunt III and S. S. Ravi, "The Complexity of Approximating PSPACE-Complete Problems for Hierarchical Specifications," Nordic J. Computing, Vol. 1, 1994, pp. 275--316.

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M.V. Marathe, H.B. Hunt III, and S.S. Ravi, "The Complexity of Approximating PSPACEComplete Problems for Hierarchical Specifications," Nordic Journal of Computing, Vol. 1, 1994, pp. 275-316.

....finding polynomial time approximation algorithms with provable worst case guarantees for NP hard problems. In contrast, until recently little work has been done towards investigating the existence of polynomial time approximation algorithms for PSPACE hard problems. As a step in this direction, in [40, 41] we have investigated the existence and non existence of polynomial time approximations for several PSPACE hard problems for L specified graphs. In [20] we considered geometric intersection graphs defined using the hierarchical specifications (HIL) of Bentley, Ottmann and Widmayer [5] There, we ....

....4.2 depicts the graph E(G) specified by G. The correspondence between pins of G j and neighbors of G j in G i , j i, is clear by the positions of the vertices and the pins. 2 4.1. Level restricted specifications. We discuss level restricted L specifications now. This is also discussed in [40, 41]. Definition 4.4. An L specification Gamma = G 1 ; Gn ) n 1) of a graph G is 1 level restricted, if for all edges (u; v)of E ( Gamma) either (1) n u and n v are the same vertex of HT ( Gamma) or (2) one of n u or n v is the parent of the other in HT ( Gamma) Extending the above ....

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M.V. Marathe H.B. Hunt III, and S.S. Ravi, The Complexity of Approximating PSPACEComplete Problems for Hierarchical Specifications, Nordic Journal of Computing, Vol. 1, 1994, pp. 275-316.

....finding polynomial time approximation algorithms with provable worst case guarantees for NP hard problems. In contrast, until recently little work has been done towards investigating the existence of polynomial time approximation algorithms for PSPACE hard problems. As a step in this direction, in [40, 41] we have investigated the existence and nonexistence of polynomial time approximations for several PSPACE hard problems for L specified graphs. In [20] we considered geometric intersection graphs defined using the hierarchical specifications (HIL) of Bentley, Ottmann, and Widmayer [5] There, we ....

....Figure 4.2 depicts the graph E(G) specified by G. The correspondence between pins of G j and neighbors of G j in G i , j i, is clear by the positions of the vertices and the pins. 4.1. Level restricted specifications. We discuss level restricted L specifications now. This is also discussed in [40, 41]. Definition 4.4. An L specification # = G 1 , G n ) n # 1, of a graph G is 1 level restricted if for all edges (u, v)of E(#) either 1. n u and n v are the same vertex of HT(#) or 2. one of n u or n v is the parent of the other in HT(#) Extending the above definition we can ....

[Article contains additional citation context not shown here]

<F3.764e+05> M.V. Marathe H.B. Hunt III, and S.S.<F3.854e+05> Ravi,<F3.516e+05> The complexity of approximating PSPACEcomplete problems for hierarchical<F3.854e+05> specifications, Nordic J. Comput., 1 (1994), pp. 275--316.

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