Affiliation:
1. Univ. of California at San Diego, La Jolla
2. AT&T Bell Labs, Murray Hill, NJ
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
O
(log
n
) 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:
O
(
n
log
n
+
m
) for the single-source shortest path problem with nonnegative edge lengths, improved from
O
(
m
log
(
m/n
+2)
n
);
O
(
n
2
log
n
+
nm
) for the all-pairs shortest path problem, improved from
O
(
nm
log
(
m/n
+2)
n
);
O
(
n
2
log
n
+
nm
) for the assignment problem (weighted bipartite matching), improved from
O
(
nm
log
(
m/n
+2)
n
);
O
(
mβ
(
m, n
)) for the minimum spanning tree problem, improved from
O
(
m
log log
(
m/n
+2)
n
); where
β
(
m, n
) = min {
i
| log
(
i
)
n
≤
m/n
}. Note that
β
(
m, n
) ≤ log
*
n
if
m
≥
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference28 articles.
1. AHO A. V. HOPCROFT J. E. AND ULLMAN J. D. The Design and Analysis of Computer Algorithms. Addison-Wesley Reading Mass. 1974. AHO A. V. HOPCROFT J. E. AND ULLMAN J. D. The Design and Analysis of Computer Algorithms. Addison-Wesley Reading Mass. 1974.
2. Implementation and Analysis of Binomial Queue Algorithms
3. A note on finding optimum branchings
4. Finding Minimum Spanning Trees
5. A note on two problems in connexion with graphs
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