An incremental linear-time algorithm for recognizing interval graphs
SIAM Journal on Computing
On the complexity of graph reconstruction
Mathematical Systems Theory
A Linear Time Algorithm for Deciding Interval Graph Isomorphism
Journal of the ACM (JACM)
Journal of Computer and System Sciences
Reconstruction of interval graphs
Theoretical Computer Science
Reconstruction algorithm for permutation graphs
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
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The graph reconstruction conjecture is a long-standing open problem in graph theory. There are many algorithmic studies related it besides mathematical studies, such as DECK CHECKING, LEGITIMATE DECK, PREIMAGE CONSTRUCTION, and PREIMAGE COUNTING. We study these algorithmic problems limiting the graph class to interval graphs. Since we can solve GRAPH ISOMORPHISM for interval graphs in polynomial time, DECK CHECKING for interval graphs is easily done in polynomial time. Since the number of interval graphs that can be obtained from an interval graph by adding a vertex and edges incident to it can be exponentially large, developing polynomial time algorithms for LEGITIMATE DECK, PREIMAGE CONSTRUCTION, and PREIMAGE COUNTING on interval graphs is not trivial. We present that these three problems are solvable in polynomial time on interval graphs.