The geometric maximum traveling salesman problem
Journal of the ACM (JACM)
Faster and better global placement by a new transportation algorithm
Proceedings of the 42nd annual Design Automation Conference
The averaged mappings problem: statement, applications, and approximate solution
Proceedings of the 44th annual Southeast regional conference
M-description lattice vector quantization: index assignment and analysis
IEEE Transactions on Signal Processing
Using combinatorial optimization in model-based trimmed clustering with cardinality constraints
Computational Statistics & Data Analysis
A faster polynomial algorithm for the unbalanced Hitchcock transportation problem
Operations Research Letters
Geometric quadrisection in linear time, with application to VLSI placement
Discrete Optimization
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We consider the Hitchcock transportation problem on $n$ supply points and $k$ demand points when $n$ is much greater than $k$. The problem can be solved in $O(k n^2 \log n + n^2 \log^2 n)$ time if an efficient minimum-cost flow algorithm is directly applied. Applying a geometric method named splitter finding and a randomization technique, we can improve the time complexity when the ratio $c$ of the maximum supply to the minimum supply is sufficiently small. The expected running time of our randomized algorithm is $O(\frac{kn \log cn}{\log (n/k^4 \log^{2}k)})$ if $n k^4 \log^{2} k$, and $O(k^5 \log^{2} n \log cn)$ if $n \le k^4 \log^{2} k$. If $n = \Omega(k^{4 + \epsilon})\ (\epsilon 0)$ and $c = \mbox{poly}(n)$, the problem is solved in $O(kn)$ time, which is optimal.