相关论文: Average-Case Complexity of Shellsort

Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…

The \emph{generalized sorting problem} is a restricted version of standard comparison sorting where we wish to sort $n$ elements but only a subset of pairs are allowed to be compared. Formally, there is some known graph $G = (V, E)$ on the…

Motivated by the development of computer theory, the sorting algorithm is emerging in an endless stream. Inspired by decrease and conquer method, we propose a brand new sorting algorithmUltimately Heapsort. The algorithm consists of two…

We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G cong H. For several decades, the n^(log_p n + O(1)) generator-enumeration bound (where p is the smallest prime…

In a previous paper, an implementable algorithm was introduced to compute discrete solutions of sweeping processes (i.e. specific first order differential inclusions). The convergence of this numerical scheme was proved thanks to…

The complexity of the Quicksort algorithm is usually measured by the number of key comparisons used during its execution. When operating on a list of $n$ data, permuted uniformly at random, the appropriately normalized complexity $Y_n$ is…

We propose an algorithm for quickly evaluating polynomials. It pre-conditions a complex polynomial $P$ of degree $d$ in time $O(d\log d)$, with a low multiplicative constant independent of the precision. Subsequent evaluations of $P$…

This paper studies the lower bound complexity for the optimization problem whose objective function is the average of $n$ individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for…

Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense…

Sorting and hashing are two completely different concepts in computer science, and appear mutually exclusive to one another. Hashing is a search method using the data as a key to map to the location within memory, and is used for rapid…

The k-means method is one of the most widely used clustering algorithms, drawing its popularity from its speed in practice. Recently, however, it was shown to have exponential worst-case running time. In order to close the gap between…

The shellability status of previously investigated simplicial complexes with up to 24 facets is settled. In case of shellability the exact number of shellings is determined. Our algorithm merely relies on the facets, and not on additional…

Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…

We present a new analysis for QuickHeapsort splitting it into the analysis of the partition-phases and the analysis of the heap-phases. This enables us to consider samples of non-constant size for the pivot selection and leads to better…

We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that in general a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant…

This paper addresses the anytime sorting problem, aiming to develop algorithms providing tentative estimates of the sorted list at each execution step. Comparisons are treated as steps, and the Spearman's footrule metric evaluates…

We consider a broad class of first-order optimization algorithms which are \emph{oblivious}, in the sense that their step sizes are scheduled regardless of the function under consideration, except for limited side-information such as…

The linear pivot selection algorithm, known as median-of-medians, makes the worst case complexity of quicksort be $\mathrm{O}(n\ln n)$. Nevertheless, it has often been said that this algorithm is too expensive to use in quicksort. In this…

A generalization of the heapsort algorithm is proposed. At the expense of about 50% more comparison and move operations for typical cases, the dualheap sort algorithm offers several advantages over heapsort: improved cache performance,…