### The soft heap: an approximate priority queue with optimal error rateThe soft heap: an approximate priority queue with optimal error rate

Access Restriction
Subscribed

 Author Chazelle, Bernard Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2000 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Amoritization ♦ Heap ♦ Priority queue ♦ Soft heap Abstract A simple variant of a priority queue, called a soft heap, is introduced. The data structure supports the usual operations: insert, delete, meld, and findmin. Its novelty is to beat the logarithmic bound on the complexity of a heap in a comparison-based model. To break this information-theoretic barrier, the entropy of the data structure is reduced by artifically raising the values of certain keys. Given any mixed sequence of $\textit{n}$ operations, a soft heap with error rate ε (for any 0 < ε ≤ 1/2) ensures that, at any time, at most $\textit{εn}$ of its items have their keys raised. The amortized complexity of each operation is constant, except for insert, which takes $\textit{0}(log$ 1/ε)time. The soft heap is optimal for any value of ε in a comparison-based model. The data structure is purely pointer-based. No arrays are move items across the data structure not individually, as is customary, but in groups, in a data-structuring equivalent of “car pooling.” Keys must be raised as a result, in order to preserve the heap ordering of the data structure. The soft heap can be used to compute exact or approximate medians and percentiles optimally. It is also useful for approximate sorting and for computing minimum spanning trees of general graphs. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2000-11-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 47 Issue Number 6 Page Count 16 Starting Page 1012 Ending Page 1027

#### Open content in new tab

Source: ACM Digital Library