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Fibonacci Heaps and Their Uses in Improved Network . . .-英文文献
Fibonacci Heaps and Their Uses in Improved Network
Optimization Algorithms
MICHAEL L. FREDMAN
University of California, San Diego, L.a Jolla, California
AND
ROBERT ENDRE TARJAN
ATT Bell Laboratories, Murray HilI, New Jersey
Abstract. In this paper we develop a new data structure for implementing heaps (priority queues). Our
structure, Fibonacci heaps (abbreviated F-heaps), extends the binomial queues proposed by Vuillemin
and studied further by Brown. F-heaps support arbitrary deletion from an n-item heap in qlogn)
amortized time and all other standard heap operations in o( 1) amortized time. Using F-heaps we are
able to obtain improved running times for several network optimization algorithms. In particular, we
obtain the following worst-case bounds, where n is the number of vertices and m the number of edges
in the problem graph:
( 1) O(n log n + m) for the single-source shortest path problem with nonnegative edge lengths, improved
from O(mlogfmh+2)n);
(2) O(n*log n + nm) for the all-pairs shortest path problem, improved from O(nm lo,,,+2,n);
(3) O(n*logn + nm) for the assignment problem (weighted bipartite matching), improved from
O(nmlog0dn+2)n);
(4) O(mj3(m, n)) for the minimum spanning tree problem, improved from O(mloglo,,.+2,n), where
j3(m, n) = min {i 1log% 5 m/n). Note that B(m, n) 5 log*n if m 2 n.
Of these results, the improved bound for minimum spanning trees is the most striking, although all the
results give asymptotic improvements for graphs of appropriate densities.
Categories and Subject Descriptors: E.l [Data]: Data Structures--trees; graphs; F.2.2 [Anal
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