Abstract
In this paper we study the following problem, named Maximum Edges in Transitive Closure, which has applications in computational biology. Given a simple, undirected graph G = (V,E) and a coloring of the vertices, remove a collection of edges from the graph such that each connected component is colorful (i.e., it does not contain two identically colored vertices) and the number of edges in the transitive closure of the graph is maximized. The problem is known to be APX-hard, and no approximation algorithms are known for it. We improve the hardness result by showing that the problem is NP-hard to approximate within a factor of |V |1/3−ε, for any constant ε > 0. Additionally, we show that the problem is APXhard already for the case when the number of vertex colors equals 3. We complement these results by showing the first approximation algorithm for the problem, with approximation factor [formula presented].
| Original language | English |
|---|---|
| Title of host publication | Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers |
| Publisher | Springer Verlag |
| Pages | 13-23 |
| Number of pages | 11 |
| Volume | 8986 |
| ISBN (Print) | 9783319193144 |
| DOIs | |
| Publication status | Published - 2015 |
| Externally published | Yes |
| Event | 25th International Workshop on Combinatorial Algorithms, IWOCA 2014 - Duluth, United States Duration: Oct 15 2014 → Oct 17 2014 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 8986 |
| ISSN (Print) | 03029743 |
| ISSN (Electronic) | 16113349 |
Other
| Other | 25th International Workshop on Combinatorial Algorithms, IWOCA 2014 |
|---|---|
| Country | United States |
| City | Duluth |
| Period | 10/15/14 → 10/17/14 |
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ASJC Scopus subject areas
- Computer Science(all)
- Theoretical Computer Science
Cite this
Approximation and hardness results for the maximum edges in transitive closure problem. / Adamaszek, Anna; Blin, Guillaume; Popa, Alexandru.
Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers. Vol. 8986 Springer Verlag, 2015. p. 13-23 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8986).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Approximation and hardness results for the maximum edges in transitive closure problem
AU - Adamaszek, Anna
AU - Blin, Guillaume
AU - Popa, Alexandru
PY - 2015
Y1 - 2015
N2 - In this paper we study the following problem, named Maximum Edges in Transitive Closure, which has applications in computational biology. Given a simple, undirected graph G = (V,E) and a coloring of the vertices, remove a collection of edges from the graph such that each connected component is colorful (i.e., it does not contain two identically colored vertices) and the number of edges in the transitive closure of the graph is maximized. The problem is known to be APX-hard, and no approximation algorithms are known for it. We improve the hardness result by showing that the problem is NP-hard to approximate within a factor of |V |1/3−ε, for any constant ε > 0. Additionally, we show that the problem is APXhard already for the case when the number of vertex colors equals 3. We complement these results by showing the first approximation algorithm for the problem, with approximation factor [formula presented].
AB - In this paper we study the following problem, named Maximum Edges in Transitive Closure, which has applications in computational biology. Given a simple, undirected graph G = (V,E) and a coloring of the vertices, remove a collection of edges from the graph such that each connected component is colorful (i.e., it does not contain two identically colored vertices) and the number of edges in the transitive closure of the graph is maximized. The problem is known to be APX-hard, and no approximation algorithms are known for it. We improve the hardness result by showing that the problem is NP-hard to approximate within a factor of |V |1/3−ε, for any constant ε > 0. Additionally, we show that the problem is APXhard already for the case when the number of vertex colors equals 3. We complement these results by showing the first approximation algorithm for the problem, with approximation factor [formula presented].
UR - http://www.scopus.com/inward/record.url?scp=84937394799&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84937394799&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-19315-1_2
DO - 10.1007/978-3-319-19315-1_2
M3 - Conference contribution
SN - 9783319193144
VL - 8986
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 13
EP - 23
BT - Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers
PB - Springer Verlag
ER -