Results 1 
4 of
4
A Tight Lower Bound for Online Monotonic List Labeling
 In SWAT
, 1994
"... . Maintaining a monotonic labeling of an ordered list during the insertion of n items requires\Omega (n log n) individual relabelings, in the worst case, if the number of usable labels is only polynomial in n. This follows from a lower bound for a new problem, prefix bucketing. 1. Introduction The ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
. Maintaining a monotonic labeling of an ordered list during the insertion of n items requires\Omega (n log n) individual relabelings, in the worst case, if the number of usable labels is only polynomial in n. This follows from a lower bound for a new problem, prefix bucketing. 1. Introduction The online listlabeling problem can be viewed as one of linear density control. A sequence of n distinct items from some dense, linearly ordered set, such as the real numbers, is received one at a time, in no predictable order. Using "labels" from some discrete linearly ordered set of adequate but limited cardinality, the problem is to maintain an assignment of labels to the items received so far, so that the labels are ordered in the same way as the items they label. In order to make room for the next item received, it might be necessary to change the labels assigned to some of the items previously received. The cost is the total number of labelings and relabelings performed. There are practi...
The complexity of constructing evolutionary trees using experiments
, 2001
"... We present tight upper and lower bounds for the problem of constructing evolutionary trees in the experiment model. We describe an algorithm which constructs an evolutionary tree of n species in time O(nd log d n) using at most n⌈d/2⌉(log 2⌈d/2⌉−1 n+O(1)) experiments for d> 2, and at most n(log n+ ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
We present tight upper and lower bounds for the problem of constructing evolutionary trees in the experiment model. We describe an algorithm which constructs an evolutionary tree of n species in time O(nd log d n) using at most n⌈d/2⌉(log 2⌈d/2⌉−1 n+O(1)) experiments for d> 2, and at most n(log n+O(1)) experiments for d = 2, where d is the degree of the tree. This improves the previous best upper bound by a factor Θ(log d). For d = 2 the previously best algorithm with running time O(n log n) had a bound of 4n log n on the number of experiments. By an explicit adversary argument, we show an Ω(nd log d n) lower bound, matching our upper bounds and improving the previous best lower bound by a factor Θ(log d n). Central to our algorithm is the construction and maintenance of separator trees of small height, which may be of independent interest.
Binary search trees: How low can you go?
 SWAT'96, LNCS
, 1996
"... We prove that no algorithm for balanced binary search trees performing insertions and deletions in amortized time O(f(n)) can guarantee a height smaller than dlog(n + 1) + 1=f(n)e for all n. We improve the existing upper bound to dlog(n + 1) + log 2 (f(n))=f(n)e, thus almost matching our lower boun ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We prove that no algorithm for balanced binary search trees performing insertions and deletions in amortized time O(f(n)) can guarantee a height smaller than dlog(n + 1) + 1=f(n)e for all n. We improve the existing upper bound to dlog(n + 1) + log 2 (f(n))=f(n)e, thus almost matching our lower bound. We also improve the existing upper bound for worst case algorithms, and give a lower bound for the semidynamic case.
A HeapBased Optimal InversionsSensitive Sorting Algorithm
, 2003
"... this paper, we describe a new timeoptimal algorithm that makes n lg(I=n) + O(n lg lg(I=n) + n) comparisons. This is an optimal algorithm for inversionssensitive sorting in the sense that it is timeoptimal and the number of comparisons it performs matches the informationtheoretic lower bound up t ..."
Abstract
 Add to MetaCart
this paper, we describe a new timeoptimal algorithm that makes n lg(I=n) + O(n lg lg(I=n) + n) comparisons. This is an optimal algorithm for inversionssensitive sorting in the sense that it is timeoptimal and the number of comparisons it performs matches the informationtheoretic lower bound up to lower order terms. (To be precise, the number of comparisons performed by our algorithm is optimal with respect to its leading term and near optimal with respect to the second term. This is explained in the following section.) 2 Earlier Results Adaptive sorting using the nger trees data structure introduced in [GMPR77], was the rst inversionssensitive timeoptimal sorting algorithm. Mehlhorn [Me79] introduced an algorithm with the same time bounds as nger trees. Both of these algorithms are considered impractical. As summarized by Elmasry [El02], other algorithms that are timeoptimal and inversionssensitive are Blocksort [LP96] which runs in place and treebased Mergesort [MEP96] which is timeoptimal with respect to several other measures of presortedness