https://hal.inria.fr/hal-00959022Chen, Hon-ChanHon-ChanChenDepartment of Information Management [Taichung] - National Taichung University of Science and TechnologyOptimal Sequential and Parallel Algorithms for Cut Vertices and Bridges on Trapezoid GraphsHAL CCSD2004cut vertexbridgetrapezoid graphalgorithm[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Inria Sophia Antipolis-MÃ©diterranÃ©e / I3s, Service Ist2014-03-13 17:06:442017-11-29 10:26:202014-03-13 21:14:01enJournal articleshttps://hal.inria.fr/hal-00959022/document10.46298/dmtcs.314application/pdf1Let G be a graph. A component of G is a maximal connected subgraph in G. A vertex v is a cut vertex of G if k(G-v) > k(G), where k(G) is the number of components in G. Similarly, an edge e is a bridge of G if k(G-e) > k(G). In this paper, we will propose new O(n) algorithms for finding cut vertices and bridges of a trapezoid graph, assuming the trapezoid diagram is given. Our algorithms can be easily parallelized on the EREW PRAM computational model so that cut vertices and bridges can be found in O(log n) time by using O(n / log n) processors.