M. Tompa. Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations. SIAM Journal on Computing, 11(1):130--137, Feb. 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in the graph. At the other extreme, Savitch s algorithm [Sav70] requires only O(log 2 n) space which is currently the smallest space achievable. The main drawback is, however, that it takes 2 O(log 2 n) time. Nevertheless, these two results imply that stcon is in P Polylogspace. Tompa [Tom82] shows that a certain natural approach, repeated squaring, for computing stcon has no implementation which runs in polynomial time and sub linear space simultaneously. However, Barnes et al. BBRS92] construct an algorithm which uses only n=2 Omega Gamma p log n) space (which is sub linear) ....

Martin Tompa. Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations. SIAM Journal on Computing, 11(1):130--137, February 1982.

....search, which, when combined with the third, gives a sublinear space, polynomial time algorithm for stcon. Again, no previously known deterministic algorithm for stcon achieved simultaneous polynomial time and sublinear space. The result is somewhat surprising given the work of Tompa [Tom82] who showed that such an algorithm is impossible for certain common approaches to solving stcon. The third tradeoff solves the short paths problem, a variant of stcon where we assume the distance from s to t is short (at most f(n) for some f(n) o(n) We are not aware of any previous ....

....on their JAG model, closely matching Savitch s upper bound. Berman and Simon [BS83] extend this result to give a similar lower bound on a randomized version of the JAG. Beame et al. BBR 90] give time space lower bounds for ustcon on more restricted versions of the JAG model. Finally, Tompa [Tom82] shows that for certain natural approaches to solving stcon, performance degrades sharply with decreasing space: space o(n) implies superpolynomial time, and space n 10ffl for fixed ffl 0 implies time n Omega log n) essentially as slow as Savitch s algorithm. It has been conjectured ....

M. Tompa. Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations. SIAM Journal on Computing, 11(1):130--137, February 1982.

....time and space requirements of algorithms for directed connectivity. No nontrivial lower bounds are known for general models of computation (such as Turing machines) on either the space, or on the simultaneous space and time required to solve stcon, although Cook and Rackoff [3] and Tompa [8] have obtained lower bounds for restricted models. This paper presents new upper bounds for the problem. The standard algorithms for connectivity, breadth and depth first search, run in optimal time Theta(m n) and use Theta(n log n) space. At the other extreme, Savitch s Theorem [7] provides ....

....there was no corresponding sublinear space, polynomial time algorithm known for stcon, and there was some evidence 2 suggesting that none was possible. It has been conjectured [2] that no deterministic stcon algorithm can run in simultaneous polynomial time and polylogarithmic space. Tompa [8] shows that certain natural approaches to solving stcon admit no such solution. Indeed, he shows that for these approaches, performance degrades sharply with decreasing space. Space o(n) implies superpolynomial time, and space n 1 Gammaffl for fixed ffl 0 implies time n Omega Gamma118 n) ....

M. Tompa. Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations. SIAM Journal on Computing, 11(1):130--137, Feb. 1982.

....pebbles are located. Cook and Racko# [11] prove a lower bound of #(log 2 n log log n) on the space required for a JAG to compute directed st connectivity (stcon) Berman and Simon [8] extend this result to randomized JAGs, and Poon [18] extends it to a probabilistic version of the NNJAG. Tompa [23] shows lower bounds on the product of the time and space needed when using certain natural approaches to solve stcon. Many time space lower bounds have been proved for undirected st connectivity (ustcon) on various weak versions of the JAG model [7, 10, 11] Edmonds was the first to prove a ....

<F3.734e+05> M.<F3.811e+05> Tompa,<F3.365e+05> Two familiar transitive closure algorithms which admit no polynomial time, sublinear space<F3.811e+05> implementations, SIAM J. Comput., 11 (1982), pp. 130--137.

....used algorithms for st connectivity, breadth and depth first search run in optimal time O(m n) and use O(n log n) space. At the other extreme, Savitch [28] provided an algorithm that uses O(log 2 n) space and requires time exponential in its space bound (i.e. time n O(log n) Tompa [30] showed that stcon cannot be solved in polynomial time and sublinear space simultaneously by the repeated squaring method. However, Barnes et al. 3] gave a polynomial time algorithm for stcon that uses space S # n 2 #( # log n) providing the first polynomial time, sublinear space algorithm. ....

<F3.748e+05> M.<F3.815e+05> Tompa,<F3.419e+05> Two familiar transitive closure algorithms which admit no polynomial time, sublinear space<F3.815e+05> implementations, SIAM J. Comput., 11 (1982), pp. 130--137.

....time and space requirements of algorithms for directed connectivity. No nontrivial lower bounds are known for general models of computation (such as Turing machines) on either the space, or on the simultaneous space and time required to solve stcon, although Cook and Rackoff [3] and Tompa [8] have obtained lower bounds for restricted models. This paper presents new upper bounds for the problem. The standard algorithms for connectivity, breadth and depth first search, run in optimal time 2(m n) and use 2(n log n) space. At the other extreme, Savitch s Theorem [7] provides a small ....

....paper, there was no corresponding sublinear space, polynomial time algorithm known for stcon, and there was some evidence suggesting that none was possible. It has been conjectured [2] that no deterministic stcon algorithm can run in simultaneous polynomial time and polylogarithmic space. Tompa [8] shows that certain natural approaches to solving stcon admit no such solution. Indeed, he shows that for these approaches, performance degrades sharply with decreasing space: space o(n) implies superpolynomial time, and space n 10ffl for fixed ffl 0 implies time n Omega log n) ....

M. Tompa. Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations. SIAM Journal on Computing, 11(1):130--137, Feb. 1982.

....common algorithms for st connectivity, breadth and depth first search run in optimal time O(m n) and use O(n log n) space. At the other extreme, Savitch [Sav70] provided an algorithm that uses O(log 2 n) space and requires time exponential in its space bound (i.e. time n O(logn) Tompa [Tom82] showed that stcon cannot be solved in polynomial time and sublinear space simultaneously by the repeated squaring method. However, Barnes et al. BBRS92] gave a polynomial time algorithm for stcon that uses space S 2 n=2 Theta( p log n) providing the first polynomial time, sub linear ....

Martin Tompa. Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations. SIAM Journal on Computing, 11(1):130--137, February 1982.

....n 2(logn) A similar but more subtle algorithm by Cook and Rackoff [11] for their more restricted JAG model has essentially the same performance. No sublinear space, polynomial time algorithm is known for stcon, and there is evidence suggesting that none is possible. Specifically, Tompa [24] has shown that certain natural approaches to solving stcon admit no such solution. Indeed, he shows that for these approaches, performance degrades sharply with decreasing space: space o(n) implies time n Omega log n) essentially as slow as Savitch s algorithm. Proving a nonpolynomial time ....

M. Tompa. Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations. SIAM Journal on Computing, 11(1):130--137, Feb. 1982.

....and Rackoff [8] prove a lower bound of Omega Gamma log 2 n= log log n Delta on the space required for a JAG to compute directed s t connectivity (stcon) Berman and Simon [3] extend this result to randomized JAGs, and Poon [13] extends it to a probabilistic version of the NNJAG. Tompa [17] shows lower bounds on the product of the time and space needed when using certain natural approaches to solve stcon. Many time space lower bounds have been proved for undirected s t connectivity on various weak versions of the JAG model [2, 7, 8] Edmonds was the first to prove a time space ....

M. Tompa. Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations. SIAM Journal on Computing, 11(1):130--137, Feb. 1982.

....space bounded algorithms. For instance, although directed graphs can be traversed nondeterministically in polynomial time and logarithmic space simultaneously, it is not widely believed that they can be traversed deterministically in polynomial time and small space simultaneously. See Tompa [32] and Edmonds and Poon [22] for lower bounds, and Barnes et al. 5] for an upper bound. In contrast, undirected graphs can be traversed in polynomial time and logarithmic space probabilistically by using a random walk (Aleliunas et al. 2] Borodin et al. 15] this implies similar resource ....

M. Tompa. Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations. SIAM Journal on Computing, 11(1):130--137, Feb. 1982.

....space bounded algorithms. For instance, although directed graphs can be traversed nondeterministically in polynomial time and logarithmic space simultaneously, it is not widely believed that they can be traversed deterministically in polynomial time and small space simultaneously. See Tompa [48] and Edmonds and Poon [27] for lower bounds, and Barnes et al. 5] for an upper bound. In contrast, undirected graphs can be traversed in polynomial time and logarithmic space probabilistically by using a random walk (Aleliunas et al. 2] Borodin et al. 17] this implies similar resource ....

M. Tompa. Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations. SIAM Journal on Computing, 11(1):130--137, Feb. 1982.

....space bounded algorithms. For instance, although directed graphs can be traversed nondeterministically in polynomial time and logarithmic space simultaneously, it is not widely believed that they can be traversed deterministically in polynomial time and small space simultaneously. See Tompa [35] for a lower bound, and Barnes et al. 5] for an upper bound. In contrast, undirected graphs can be traversed in polynomial time and logarithmic space probabilistically by using a random walk (Aleliunas et al. 2] Borodin et al. 13] this implies similar resource bounds on (nonuniform) ....

M. Tompa. Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations. SIAM Journal on Computing, 11(1):130--137, Feb. 1982.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC