TY - JOUR

T1 - Soft heaps simplified

AU - Kaplan, Haim

AU - Tarjan, Robert E.

AU - Zwick, Uri

PY - 2013

Y1 - 2013

N2 - In 1998, Chazelle [J. ACM, 47 (2000), pp. 1012-1027] introduced a new kind of meldable heap (priority queue) called the soft heap. Soft heaps trade accuracy for speed: the heap operations are allowed to increase the keys of certain items, thereby making these items bad, as long as the number of bad items in the data structure is at most εm, where m is the total number of insertions performed so far, and ε is an error parameter. The amortized time per heap operation is O(lg 1/ε), reduced from O(lgn), where n is the number of items in the heap. Chazelle used soft heaps in several applications, including a faster deterministic minimum-spanning-tree algorithm and a new deterministic linear-time selection algorithm. We give a simplified implementation of soft heaps that uses less space and avoids Chazelle's dismantling operations. We also give a simpler, improved analysis that yields an amortized time bound of O(lg 1/ε) for each deletion, O(1) for each other operation.

AB - In 1998, Chazelle [J. ACM, 47 (2000), pp. 1012-1027] introduced a new kind of meldable heap (priority queue) called the soft heap. Soft heaps trade accuracy for speed: the heap operations are allowed to increase the keys of certain items, thereby making these items bad, as long as the number of bad items in the data structure is at most εm, where m is the total number of insertions performed so far, and ε is an error parameter. The amortized time per heap operation is O(lg 1/ε), reduced from O(lgn), where n is the number of items in the heap. Chazelle used soft heaps in several applications, including a faster deterministic minimum-spanning-tree algorithm and a new deterministic linear-time selection algorithm. We give a simplified implementation of soft heaps that uses less space and avoids Chazelle's dismantling operations. We also give a simpler, improved analysis that yields an amortized time bound of O(lg 1/ε) for each deletion, O(1) for each other operation.

KW - Data structures

KW - Heaps

KW - Priority queues

UR - http://www.scopus.com/inward/record.url?scp=84884970030&partnerID=8YFLogxK

U2 - 10.1137/120880185

DO - 10.1137/120880185

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AN - SCOPUS:84884970030

SN - 0097-5397

VL - 42

SP - 1660

EP - 1673

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 4

ER -