1 The problem of sorting an intransitive total ordered set, a generalization of regular sorting, is considered. This generalized sorting is based on the fact that there exists a special linear ordering for any intransitive total ordered set. A new data structure called semi-heap is proposed to construct an optimal (n logn) sorting algorithm. Finally, we propose a cost-optimal parallel algorithm...

We study the selection problem, namely that of computing the ith order statistic of n given elements. Here we offer a data structure called selectable sloppy heap handling a dynamic version in which upon request: (i) a new element is inserted or (ii) an element of a prescribed quantile group is deleted from the data structure. Each operation is executed in (ideal!) constant time— and is thus in...

An algorithmic computation of the set of unpointed stable homotopy classes of equivariant fibrewise maps was described in a recent paper [4] of the author and his collaborators. In the present paper, we describe a simplification of this computation that uses an abelian heap structure on this set that was observed in another paper [5] of the author. A heap is essentially a group without a choice...

In this lecture we extend our language with the ability to allocate data structures on the so-called heap. Addresses of heap elements serve as pointers which can be dereferenced to read stored values, or used as destinations for write operations. Similarly, arrays are stored on the heap1 and via appropriate address calculations. Adding mutable store requires yet again a significant change in th...

In this paper we explore two themes in data structure design: amortized computational complexity and self-adjustment. We are motivated by the following observations. In most applications of data structures, we wish to perform not just a single operation but a sequence of operations, possibly having correlated behavior. By averaging the running time per operation over a worst-case sequence of op...

Per-ow queueing with sophisticated scheduling is a candidate architecture for networks that provide advanced Quality-of-Service (QoS) guarantees. The hardest and most interesting scheduling algorithms rely on a common computational primitive: priority queues. Large priority queues are built using calendar queue or heap data structures. To support such scheduling for a large number of ows at OC-...

A data structure is stabilizing if, for any arbitrary (and possibly illegitimate) initial state, any sequence of sufficiently many operations brings the data structure to a legitimate state. A data structure is available if, for any arbitrary state, the effect of any operation on the structure is consistent with the operation’s response. This paper presents an available stabilizing data structu...

Separation logic is an extension of Hoare logic which permits reasoning about low-level imperative programs that use shared mutable heap structure. In this work, we present a version of separation logic that permits effective, modular reasoning about typed, higherorder functional programs that use aliased mutable heap data, including pointers to code. Furthermore, we show how to use predicates ...

In [8] a new data structure called semi-heap is proposed to construct an optimal (n logn) sorting algorithm to sort an intransitive total ordered set, a generalization of regular sorting. In this part, we provide a cost-optimal parallel algorithm using semi-heap. The run time of this algorithm is (n) with (logn) processors under the EREW PRAM model. The use of a Hamiltonian path (generalized so...