TY - JOUR
T1 - Parallelism and the maximal path problem
AU - Anderson, Richard
AU - Mayr, Ernst W.
PY - 1987/1/30
Y1 - 1987/1/30
N2 - The maximal path problem is the following: Given a graph G = (V, E) and a vertex r, find a path starting at r that cannot be extended without encountering a node that is already on the path. We shall show that if all nodes have degree at most D(n), the problem can be solved in O(D(n) log3 n) time using O(n2) processors. We also obtain an NC algorithm for the maximal path problem in planar graphs. Finally, we show that the problem of computing the lexicographically minimal maximal path is P-complete, even when restricted to planar graphs.
AB - The maximal path problem is the following: Given a graph G = (V, E) and a vertex r, find a path starting at r that cannot be extended without encountering a node that is already on the path. We shall show that if all nodes have degree at most D(n), the problem can be solved in O(D(n) log3 n) time using O(n2) processors. We also obtain an NC algorithm for the maximal path problem in planar graphs. Finally, we show that the problem of computing the lexicographically minimal maximal path is P-complete, even when restricted to planar graphs.
KW - Computational complexity
KW - P-completeness
KW - maximal path problem
KW - parallel algorithm
UR - http://www.scopus.com/inward/record.url?scp=0023104388&partnerID=8YFLogxK
U2 - 10.1016/0020-0190(87)90105-0
DO - 10.1016/0020-0190(87)90105-0
M3 - Article
AN - SCOPUS:0023104388
SN - 0020-0190
VL - 24
SP - 121
EP - 126
JO - Information Processing Letters
JF - Information Processing Letters
IS - 2
ER -