Abstract
We introduce a generalization of the graph isomorphism problem. Given two graphs G
1 = (V
1, E
1) and G
2 = (V
2, E
2) and two integers l and d, we seek for a one-to-one mapping f:V
1 → V
2, such that for every v ∈ V
1, it holds that L′
v
− L
v
≤ d, where 
, 
, and \(N^i_{G}(v)\) denotes the set of vertices which have distance at most i to v in a graph G. We call this problem Compactness-Preserving Mapping (CPM). In the paper we study CPM with input graphs being trees and present a dichotomy of classical complexity with respect to different values of l and d. CPM on trees can be solved in polynomial time only if l ≤ 2 and d ≤ 1.
Supported by the DFG Excellence Cluster MMCI and the International Max Planck Research School.
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Baumbach, J., Guo, J., Ibragimov, R. (2014). Compactness-Preserving Mapping on Trees. In: Kulikov, A.S., Kuznetsov, S.O., Pevzner, P. (eds) Combinatorial Pattern Matching. CPM 2014. Lecture Notes in Computer Science, vol 8486. Springer, Cham. https://doi.org/10.1007/978-3-319-07566-2_17
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DOI: https://doi.org/10.1007/978-3-319-07566-2_17
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