Analysis of the impact of the number of edges in connected graphs on the computational complexity of the independent set problem
Under study is the complexity status of the independent set problem in a class of connected graphs that are defined by functional constraints on the number of edges depending on the number of vertices. For every natural number C , this problem is shown to be polynomially solvable in the class of gra...
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| Vydané v: | Journal of applied and industrial mathematics Ročník 6; číslo 1; s. 97 - 99 |
|---|---|
| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
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Dordrecht
SP MAIK Nauka/Interperiodica
01.01.2012
Springer Nature B.V |
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| ISSN: | 1990-4789, 1990-4797 |
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| Abstract | Under study is the complexity status of the independent set problem in a class of connected graphs that are defined by functional constraints on the number of edges depending on the number of vertices. For every natural number
C
, this problem is shown to be polynomially solvable in the class of graphs
On the other hand, this problem is proved to be not polynomially solvable in the class of graphs
for every unbounded nondecreasing function
f
(
n
): ℕ → ℕ, such that exponent of this function grows faster than a polynomial function of
n
. The latter result is true if there does not exist a subexponential algorithm for solving the independent set problem. |
|---|---|
| AbstractList | Under study is the complexity status of the independent set problem in a class of connected graphs that are defined by functional constraints on the number of edges depending on the number of vertices. For every natural number C, this problem is shown to be polynomially solvable in the class of graphs limits n = 1 ∞ { G : ∣ V ( G ) ∣ = n , ∣ E ( G ) ∣ n + C [ log 2 ( n ) ] } . On the other hand, this problem is proved to be not polynomially solvable in the class of graphs limits n = 1 ∞ { G : ∣ V ( G ) ∣ = n , ∣ E ( G ) ∣ n + f 2 ( n ) } for every unbounded nondecreasing function f(n): [arrow right] , such that exponent of this function grows faster than a polynomial function of n. The latter result is true if there does not exist a subexponential algorithm for solving the independent set problem.[PUBLICATION ABSTRACT] Under study is the complexity status of the independent set problem in a class of connected graphs that are defined by functional constraints on the number of edges depending on the number of vertices. For every natural number C , this problem is shown to be polynomially solvable in the class of graphs On the other hand, this problem is proved to be not polynomially solvable in the class of graphs for every unbounded nondecreasing function f ( n ): ℕ → ℕ, such that exponent of this function grows faster than a polynomial function of n . The latter result is true if there does not exist a subexponential algorithm for solving the independent set problem. Under study is the complexity status of the independent set problem in a class of connected graphs that are defined by functional constraints on the number of edges depending on the number of vertices. For every natural number C, this problem is shown to be polynomially solvable in the class of graphs [intersection] limits n = 1 infinity { G : [mid] V ( G ) [mid] = n , [mid] E ( G ) [mid] [el] n + C [ log 2 ( n ) ] } . On the other hand, this problem is proved to be not polynomially solvable in the class of graphs [intersection] limits n = 1 infinity { G : [mid] V ( G ) [mid] = n , [mid] E ( G ) [mid] [el] n + f 2 ( n ) } for every unbounded nondecreasing function f(n): arrow right , such that exponent of this function grows faster than a polynomial function of n. The latter result is true if there does not exist a subexponential algorithm for solving the independent set problem. |
| Author | Malyshev, D. S. |
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| Cites_doi | 10.1006/jcss.2001.1774 |
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| DOI | 10.1134/S1990478912010103 |
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| Keywords | computational complexity independent set problem |
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| References | Malyshev (CR1) 2010 Impagliazzo, Paturi (CR3) 2001; 62 Aho, Hopcroft, Ullman (CR2) 1974 R. Impagliazzo (4204_CR3) 2001; 62 A. V. Aho (4204_CR2) 1974 D. S. Malyshev (4204_CR1) 2010 |
| References_xml | – year: 1974 ident: CR2 publication-title: The Design and Analysis of Computer Algorithms – volume: 62 start-page: 512 year: 2001 end-page: 530 ident: CR3 article-title: Which Problems Have Strongly Exponential Complexity? publication-title: J. Comput. System Sci. doi: 10.1006/jcss.2001.1774 – start-page: 136 year: 2010 ident: CR1 article-title: Joint Influence of the Number of Edges and the Component Connectedness in Graphs on the Complexity of the Independence Number Calculation publication-title: ( – volume: 62 start-page: 512 year: 2001 ident: 4204_CR3 publication-title: J. Comput. System Sci. doi: 10.1006/jcss.2001.1774 – volume-title: The Design and Analysis of Computer Algorithms year: 1974 ident: 4204_CR2 – start-page: 136 volume-title: Proceedings of the Russian Conference “Discrete Optimization and Operation Research” (The Altai Republic year: 2010 ident: 4204_CR1 |
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| Title | Analysis of the impact of the number of edges in connected graphs on the computational complexity of the independent set problem |
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