A graph G=(V,E) can be described by the characteristic function of the
edge set χE which maps a pair of binary encoded nodes to 1 iff the nodes
are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store
χE can lead to a (hopefully) compact representation. Given the OBDD as an
input, symbolic/implicit OBDD-based graph algorithms can solve optimization
problems by mainly using functional operations, e.g. quantification or binary
synthesis. While the OBDD representation size can not be small in general, it
can be provable small for special graph classes and then also lead to fast
algorithms. In this paper, we show that the OBDD size of unit interval graphs
is O(∣V∣/log∣V∣) and the OBDD size of interval graphs is $O(\
| V \ | \log \ | V \ |)whichbothimproveaknownresultfromNunkesserandWoelfel(2009).Furthermore,wecanshowthatusingourvariableorderandnodelabelingforintervalgraphstheworst−caseOBDDsizeis\Omega(\ | V \ | \log
\ | V \ |).Weusethestructureoftheadjacencymatricestoprovethesebounds.Thismethodmaybeofindependentinterestandcanbeappliedtoothergraphclasses.WealsodevelopamaximummatchingalgorithmonunitintervalgraphsusingO(\log \ | V \ |)operationsandacoloringalgorithmforunitandgeneralintervalsgraphsusingO(\log^2 \ | V \ |)$ operations and
evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic
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