Simple linear time recognition of unit interval graphs
Information Processing Letters
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Self-overlapping curves revisited
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A simple algorithm to find Hamiltonian cycles in proper interval graphs
Information Processing Letters
The Longest Path Problem Is Polynomial on Interval Graphs
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Signed networks in social media
Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
Predicting positive and negative links in online social networks
Proceedings of the 19th international conference on World wide web
Computing a Smallest Multilabeled Phylogenetic Tree from Rooted Triplets
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Can everybody sit closer to their friends than their enemies?
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Graph classes with structured neighborhoods and algorithmic applications
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Hi-index | 0.00 |
Signed graphs, i.e., undirected graphs with edges labelled with a plus or minus sign, are commonly used to model relationships in social networks. Recently, Kermarrec and Thraves [13] initiated the study of the problem of appropriately visualising the network: They asked whether any signed graph can be embedded into the metric space ℝl in such a manner that every vertex is closer to all its friends (neighbours via positive edges) than to all its enemies (neighbours via negative edges). Interestingly, embeddability into ℝ1 can be expressed as a purely combinatorial problem. In this paper we pursue a deeper study of this case, answering several questions posed by Kermarrec and Thraves. First, we refine the approach of Kermarrec and Thraves for the case of complete signed graphs by showing that the problem is closely related to the recognition of proper interval graphs. Second, we prove that the general case, whose polynomial-time tractability remained open, is in fact NP-complete. Finally, we provide lower and upper bounds for the time complexity of the general case: we prove that the existence of a subexponential time (in the number of vertices and edges of the input signed graph) algorithm would violate the Exponential Time Hypothesis, whereas a simple dynamic programming approach gives a running time single-exponential in the number of vertices.