TY - JOUR
T1 - Online set packing
AU - Emekj, Yuval
AU - Halldórsson, Magnús M.
AU - Mansour, Yishay
AU - Patt-Shamir, Boaz
AU - Radhakrishnan, Jaikumar
AU - Rawitz, Dror
PY - 2012
Y1 - 2012
N2 - In online set packing (OSP), elements arrive online, announcing which sets they belong to, and the algorithm needs to assign each element, upon arrival, to one of its sets. The goal is to maximize the number of sets that are assigned all their elements: a set that misses even a single element is deemed worthless. This is a natural online optimization problem that abstracts allocation of scarce compound resources, e.g., multipacket data frames in communication networks. We present a randomized competitive online algorithm for the weighted case with general capacity (namely, where sets may have different values, and elements arrive with different multiplicities). We prove a matching lower bound on the competitive ratio for any randomized online algorithm. Our bounds are expressed in terms of the maximum set size and the maximum number of sets an element belongs to. We also present refined bounds that depend on the uniformity of these parameters.
AB - In online set packing (OSP), elements arrive online, announcing which sets they belong to, and the algorithm needs to assign each element, upon arrival, to one of its sets. The goal is to maximize the number of sets that are assigned all their elements: a set that misses even a single element is deemed worthless. This is a natural online optimization problem that abstracts allocation of scarce compound resources, e.g., multipacket data frames in communication networks. We present a randomized competitive online algorithm for the weighted case with general capacity (namely, where sets may have different values, and elements arrive with different multiplicities). We prove a matching lower bound on the competitive ratio for any randomized online algorithm. Our bounds are expressed in terms of the maximum set size and the maximum number of sets an element belongs to. We also present refined bounds that depend on the uniformity of these parameters.
KW - Competitive analysis
KW - Multipacket frames
KW - Online set packing
KW - Packet fragmentation
KW - Randomized algorithm
UR - http://www.scopus.com/inward/record.url?scp=84866390635&partnerID=8YFLogxK
U2 - 10.1137/110820774
DO - 10.1137/110820774
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AN - SCOPUS:84866390635
SN - 0097-5397
VL - 41
SP - 728
EP - 746
JO - SIAM Journal on Computing
JF - SIAM Journal on Computing
IS - 4
ER -