S. Mertens. Phase transition in the number partitioning problem. Physical Review Letters, 81(20):4281--4284, 1998. Home/Search Document Not in Database Summary Related Articles Check |
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The Constrainedness of Search - Gent, Prosser, Walsh (1999) (35 citations) (Correct)
.... 2 (l) n : A phase transition in the probability of a perfect 2 way partition has been observed around = 0:96 [22, 24] Using some complex analysis based on statistical thermodynamics, Mertens predicts the location of this phase transition around a fixed value of a parameter given by O(1=nl) [40]. In m way number partitioning, we have n numbers drawn uniformly and at random from the range (0; l] and wish to find a partition into m bags with the same sum. As there are m n possible partitions of n numbers into m bags, N = n log 2 m We assume that the numbers have a sum which is an exact ....
S. Mertens. Phase transition in the number partitioning problem. http://xxx.lanl.gov/abs/cond-mat/9807077, 1998.
Computational Complexity for Physicists - Mertens (2000) Self-citation (Mertens) (Correct)
....physical systems. The control parameter is ff, the order parameter is the probability of the formula being satisfiable. Similar phase transitions have been discovered and analyzed with methods from statistical mechanics in other computational problems like VERTEX COVER [50] and NUMBER PARTITIONING [51]. ....
Stephan Mertens. Phase transition in the number partitioning problem. Phys. Rev. Lett., 81(20):4281--4284, November 1998. 29
A Complete Anytime Algorithm for Balanced Number Partitioning - Mertens (1999) (2 citations) Self-citation (Mertens) (Correct)
....of perfect partitions increases exponentially with n. The critical value n c depends on the number of bits needed to encode the x i . For the unconstrained partitioning problem n c 1 2 log 2 n c = 1 2 log 2 2 hx 2 i; 3) where h i denotes the average over the distribution of the x i [12]. The corresponding equation for the balanced partitioning problem reads [11] n c log 2 n c = log 2 q hx 2 i hxi 2 : 4) For most practical applications the x i have a nite precision and Eq. 3 resp. Eq. 4 can be applied. Theoretical investigations consider real valued i.i.d. ....
....and for a large class of real valued input distributions, the optimum partition has a median di erence of ( p n=2 n ) for the unconstrained resp. n=2 n ) for the balanced case [5] Using methods from statistical physics, the average optimum di erence has been calculated recently [12,11]. It reads opt = q 2 hx 2 i p n 2 n (5) for the unconstrained and opt = q hx 2 i hxi 2 n 2 n (6) 2 for the balanced partioning problem. These equations also describe the case of nite precision in the regime 1 n n c . For both variants of the partitioning ....
Stephan Mertens. Phase transition in the number partitioning problem. Phys. Rev. Lett., 81(20):4281-4284, November 1998.
Forma Analysis and new Heuristic Ideas for the Number.. - Berretta, Cotta, Moscato (2001) (Correct)
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S. Mertens. Phase transition in the number partitioning problem. Physical Review Letters, 81(20):4281--4284, 1998.
Algorithmic Implications of Phase Transitions - Istrate (Correct)
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S. Mertens. Phase transition in number partitioning problem. Physical Review Letters, 81:4281, 1998.
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