We consider the polymatroid packing and covering problems. The polynomial time algorithm with the best approximation bound known for either problem is the greedy algorithm, yielding guaranteed approximation factors of 1/k for polymatroid packing and H(k) for polymatroid covering, where k is the largest rank of an element in a polymatroid, and H(k)=Σi=1k 1/i is the kth Harmonic number. The main contribution of this note is to improve these bounds by slightly extending the greedy heuristics. Specifically, it will be shown how to obtain approximation factors of 2/(k+1) for packing and H(k)-1/6 for covering, generalizing some existing results on k-set packing, matroid matching, and k-set cover problems.
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Toshihiro FUJITO, "Approximating Polymatroid Packing and Covering" in IEICE TRANSACTIONS on Fundamentals,
vol. E85-A, no. 5, pp. 1066-1070, May 2002, doi: .
Abstract: We consider the polymatroid packing and covering problems. The polynomial time algorithm with the best approximation bound known for either problem is the greedy algorithm, yielding guaranteed approximation factors of 1/k for polymatroid packing and H(k) for polymatroid covering, where k is the largest rank of an element in a polymatroid, and H(k)=Σi=1k 1/i is the kth Harmonic number. The main contribution of this note is to improve these bounds by slightly extending the greedy heuristics. Specifically, it will be shown how to obtain approximation factors of 2/(k+1) for packing and H(k)-1/6 for covering, generalizing some existing results on k-set packing, matroid matching, and k-set cover problems.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e85-a_5_1066/_p
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@ARTICLE{e85-a_5_1066,
author={Toshihiro FUJITO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Approximating Polymatroid Packing and Covering},
year={2002},
volume={E85-A},
number={5},
pages={1066-1070},
abstract={We consider the polymatroid packing and covering problems. The polynomial time algorithm with the best approximation bound known for either problem is the greedy algorithm, yielding guaranteed approximation factors of 1/k for polymatroid packing and H(k) for polymatroid covering, where k is the largest rank of an element in a polymatroid, and H(k)=Σi=1k 1/i is the kth Harmonic number. The main contribution of this note is to improve these bounds by slightly extending the greedy heuristics. Specifically, it will be shown how to obtain approximation factors of 2/(k+1) for packing and H(k)-1/6 for covering, generalizing some existing results on k-set packing, matroid matching, and k-set cover problems.},
keywords={},
doi={},
ISSN={},
month={May},}
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TY - JOUR
TI - Approximating Polymatroid Packing and Covering
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1066
EP - 1070
AU - Toshihiro FUJITO
PY - 2002
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E85-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2002
AB - We consider the polymatroid packing and covering problems. The polynomial time algorithm with the best approximation bound known for either problem is the greedy algorithm, yielding guaranteed approximation factors of 1/k for polymatroid packing and H(k) for polymatroid covering, where k is the largest rank of an element in a polymatroid, and H(k)=Σi=1k 1/i is the kth Harmonic number. The main contribution of this note is to improve these bounds by slightly extending the greedy heuristics. Specifically, it will be shown how to obtain approximation factors of 2/(k+1) for packing and H(k)-1/6 for covering, generalizing some existing results on k-set packing, matroid matching, and k-set cover problems.
ER -