Realization Problems on Reachability Sequences

被引:0
|
作者
Dippel, Matthew [1 ]
Sundaram, Ravi [1 ]
Varma, Akshar [1 ]
机构
[1] Northeastern Univ, Boston, MA 02115 USA
来源
COMPUTING AND COMBINATORICS (COCOON 2020) | 2020年 / 12273卷
关键词
Reachability sequences; Graph realization; Bicriteria approximation; Strong NP-completeness; REALIZABILITY;
D O I
10.1007/978-3-030-58150-3_22
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
The classical Erdos-Gallai theorem kicked off the study of graph realizability by characterizing degree sequences. We extend this line of research by investigating realizability of directed acyclic graphs (DAGs) given both a local constraint via degree sequences and a global constraint via a sequence of reachability values (number of nodes reachable from a given node). We show that, without degree constraints, DAG reachability realization is solvable in linear time, whereas it is strongly NP-complete given upper bounds on in-degree or out-degree. After defining a suitable notion of bicriteria approximation based on consistency, we give two approximation algorithms achieving O(log n)-reachability consistency and O(log n)-degree consistency; the first, randomized, uses LP (Linear Program) rounding, while the second, deterministic, employs a k-set packing heuristic. We end with two conjectures that we hope motivate further study of realizability with reachability constraints.
引用
收藏
页码:274 / 286
页数:13
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