Spectrally robust graph isomorphism

Authors

Alexandra Kolla, College of Engineering and Applied Science
Ioannis Koutis, Department of Computer Science
Vivek Madan, Siebel School of Computing and Data Science
Ali Kemal Sinop, TOBB University of Economics and Technology

Document Type

Conference Proceeding

Publication Date

7-1-2018

Abstract

We initiate the study of spectral generalizations of the graph isomorphism problem. (a) The Spectral Graph Dominance (SGD) problem: On input of two graphs G and H does there exist a permutation π such that G π(H)? (b) The Spectrally Robust Graph Isomorphism (κ-SRGI) problem: On input of two graphs G and H, find the smallest number κ over all permutations π such that π(H) G κcπ(H) for some c. SRGI is a natural formulation of the network alignment problem that has various applications, most notably in computational biology. G cH means that for all vectors x we have x^TLGx ≤ cx^TLHx, where LG is the Laplacian G. We prove NP-hardness for SGD. We also present a κ³-approximation algorithm for SRGI for the case when both G and H are bounded-degree trees. The algorithm runs in polynomial time when κ is a constant.

Identifier

85049782838 (Scopus)

ISBN

[9783959770767]

Publication Title

Leibniz International Proceedings in Informatics Lipics

External Full Text Location

https://doi.org/10.4230/LIPIcs.ICALP.2018.84

ISSN

18688969

Volume

107

Grant

CCF-1319376

Fund Ref

Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences

Recommended Citation

Kolla, Alexandra; Koutis, Ioannis; Madan, Vivek; and Sinop, Ali Kemal, "Spectrally robust graph isomorphism" (2018). Faculty Publications. 8584.
https://digitalcommons.njit.edu/fac_pubs/8584