TY - GEN
T1 - Approximation algorithms for min-max generalization problems
AU - Berman, Piotr
AU - Raskhodnikova, Sofya
PY - 2010
Y1 - 2010
N2 - We provide improved approximation algorithms for the min-max generalization problems considered by Du, Eppstein, Goodrich, and Lueker [1]. In min-max generalization problems, the input consists of data items with weights and a lower bound wlb, and the goal is to partition individual items into groups of weight at least wlb, while minimizing the maximum weight of a group. The rules of legal partitioning are specific to a problem. Du et al. consider several problems in this vein: (1) partitioning a graph into connected subgraphs, (2) partitioning unstructured data into arbitrary classes and (3) partitioning a 2-dimensional array into non-overlapping contiguous rectangles (subarrays) that satisfy the above size requirements. We significantly improve approximation ratios for all the problems considered by Du et al., and provide additional motivation for these problems. Moreover, for the first problem, while Du et al. give approximation algorithms for specific graph families, namely, 3-connected and 4-connected planar graphs, no approximation algorithm that works for all graphs was known prior to this work.
AB - We provide improved approximation algorithms for the min-max generalization problems considered by Du, Eppstein, Goodrich, and Lueker [1]. In min-max generalization problems, the input consists of data items with weights and a lower bound wlb, and the goal is to partition individual items into groups of weight at least wlb, while minimizing the maximum weight of a group. The rules of legal partitioning are specific to a problem. Du et al. consider several problems in this vein: (1) partitioning a graph into connected subgraphs, (2) partitioning unstructured data into arbitrary classes and (3) partitioning a 2-dimensional array into non-overlapping contiguous rectangles (subarrays) that satisfy the above size requirements. We significantly improve approximation ratios for all the problems considered by Du et al., and provide additional motivation for these problems. Moreover, for the first problem, while Du et al. give approximation algorithms for specific graph families, namely, 3-connected and 4-connected planar graphs, no approximation algorithm that works for all graphs was known prior to this work.
UR - http://www.scopus.com/inward/record.url?scp=78149307631&partnerID=8YFLogxK
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U2 - 10.1007/978-3-642-15369-3_5
DO - 10.1007/978-3-642-15369-3_5
M3 - Conference contribution
AN - SCOPUS:78149307631
SN - 3642153682
SN - 9783642153686
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 53
EP - 66
BT - Approximation, Randomization, and Combinatorial Optimization
T2 - 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010
Y2 - 1 September 2010 through 3 September 2010
ER -