Hasil untuk "cs.DS"

Cláudio Carvalho, Jonas Costa, Raul Lopes et al.

An s-branching flow f in a network N = (D, u), where u is the capacity function, is a flow thatreaches every vertex in V(D) from s while loosing exactly one unit of flow in each vertex other thans. Bang-Jensen and Bessy [TCS, 2014] showed that, when every arc has capacity n − 1, a network Nadmits k arc-disjoint s-branching flows if and only if its associated digraph D contains k arc-disjoints-branchings. Thus a classical result by Edmonds stating that a digraph contains k arc-disjoints-branchings if and only if the indegree of every set X ⊆ V (D) \ {s} is at least k also characterizesthe existence of k arc-disjoint s-branching flows in those networks, suggesting that the larger thecapacities are, the closer an s-branching flow is from simply being an s-branching. This observationis further implied by results by Bang-Jensen et al. [DAM, 2016] showing that there is a polynomialalgorithm to find the flows (if they exist) when every arc has capacity n − c, for every fixed c ≥ 1,and that such an algorithm is unlikely to exist for most other choices of the capacities. In this paper,we investigate how a property that is a natural extension of the characterization by Edmonds’ relatesto the existence of k arc-disjoint s-branching flows in networks. Although this property is alwaysnecessary for the existence of the flows, we show that it is not always sufficient and that it is hardto decide if the desired flows exist even if we know beforehand that the network satisfies it. On thepositive side, we show that it guarantees the existence of the desired flows in some particular casesdepending on the choice of the capacity function or on the structure of the underlying graph of D,for example. We remark that, in those positive cases, polynomial time algorithms to find the flowscan be extracted from the constructive proofs.

Ali Çivril

We provide algorithms for the minimum 2-edge-connected spanning subgraph problem and the minimum 2-vertex-connected spanning subgraph problem with approximation ratio both $\frac{4}{3}$. Using a common theme, the algorithms and their analyses are very similar.

Marcel Jackiewicz, Adam Kasperski, Pawel Zielinski

This paper deals with the recoverable robust shortest path problem under the interval uncertainty representation. The problem is known to be strongly NP-hard and not approximable in general digraphs. Polynomial time algorithms for the problem under consideration in DAGs are proposed.

Gruia Calinescu, Hemanshu Kaul, Bahareh Kudarzi

We study the NP-complete Maximum Outerplanar Subgraph problem. The previous best known approximation ratio for this problem is 2/3. We propose a new approximation algorithm which improves the ratio to 7/10.

Oleg Mazonka

This paper describes a sufficiently simple modular multiplication algorithm, which uses only carry-save addition with bit inspection Boolean logic and without number comparison or carry propagation.

Tetto Obata

The range mode problem is a fundamental problem and there is a lot of work about it. There is also some work for the dynamic version of it and the enumerating version of it, but there is no previous research about the dynamic and enumerating version of it. We found an efficient algorithm for it.

Yotam Gafni

For finite integer squares, we consider the problem of learning a classification $I$ that respects Pareto domination. The setup is natural in dynamic programming settings. We show that a generalization of the binary search algorithm achieves an optimal $θ(n)$ worst-case run time.

Takanori Maehara, Kazutoshi Ando

This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time algorithm that finds such a representation. This algorithm achieves the optimal time complexity.

Huy L. Nguyen

In the matroid intersection problem, we are given two matroids of rank $r$ on a common ground set $E$ of $n$ elements and the goal is to find the maximum set that is independent in both matroids. In this note, we show that Cunningham's algorithm for matroid intersection can be implemented to use $O(nr\log^2(r))$ independent oracle calls.

Morteza Monemizadeh

Given a stream $\mathcal{S}$ of insertions and deletions of edges of an underlying graph $G$ (with fixed vertex set $V$ where $n=|V|$ is the number of vertices of $G$), we propose a dynamic algorithm that maintains a maximal independent set (MIS) of $G$ (at any time $t$ of the stream $\mathcal{S}$) with amortized update time $O(\log^3 n)$.

Dekel Tsur

We give a parameterized algorithm for weighted vertex cover on graphs with maximum degree 3 whose time complexity is $O^*(1.402^t)$, where $t$ is the minimum size of a vertex cover of the input graph.

Kai Han

We study the k-median and k-center problems in probabilistic graphs. We analyze the hardness of these problems, and propose several algorithms with improved approximation ratios compared with the existing proposals.

Udi Wieder

We show a new proof for the load of obtained by a Cuckoo Hashing data structure. Our proof is arguably simpler than previous proofs and allows for new generalizations. The proof first appeared in Pinkas et. al. \cite{PSWW19} in the context of a protocol for private set intersection. We present it here separately to improve its readability.

Igor S. Sergeev

We prove that the complexity of computing the table of primes between $1$ and $n$ on a multitape Turing machine is $O(n \log n)$.

Michael W. Mahoney

These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.

Amr Elmasry

We give a simple and efficient algorithm for adaptively counting inversions in a sequence of $n$ integers. Our algorithm runs in $O(n + n \sqrt{\lg{(Inv/n)}})$ time in the word-RAM model of computation, where $Inv$ is the number of inversions.

Yongwook Choi, Charles Knessl, Wojciech Szpankowski

In a recently proposed graphical compression algorithm by Choi and Szpankowski (2009), the following tree arose in the course of the analysis. The root contains n balls that are consequently distributed between two subtrees according to a simple rule: In each step, all balls independently move down to the left subtree (say with probability $p$) or the right subtree (with probability 1-$p$). A new node is created as long as there is at least one ball in that node. Furthermore, a nonnegative integer $d$ is given, and at level $d$ or greater one ball is removed from the leftmost node before the balls move down to the next level. These steps are repeated until all balls are removed (i.e., after $n+d$ steps). Observe that when $d=∞$ the above tree can be modeled as a $\textit{trie}$ that stores $n$ independent sequences generated by a memoryless source with parameter $p$. Therefore, we coin the name $(n,d)$-tries for the tree just described, and to which we often refer simply as $d$-tries. Parameters of such a tree (e.g., path length, depth, size) are described by an interesting two-dimensional recurrence (in terms of $n$ and $d$) that – to the best of our knowledge – was not analyzed before. We study it, and show how much parameters of such a $(n,d)$-trie differ from the corresponding parameters of regular tries. We use methods of analytic algorithmics, from Mellin transforms to analytic poissonization.

Eugenijus Manstavičius

We prove a total variation approximation for the distribution of component vector of a weakly logarithmic random assembly. The proof demonstrates an analytic approach based on a comparative analysis of the coefficients of two power series.

Igor Sergeev

We show new upper and lower bounds for the complexity of implementation of a sequence of Boolean matrices proposed by Kaski et al. (arXiv:1208.0554) with additive circuits.

Taha Sochi

In this article we discuss general strategies and computer algorithms to test the connectivity of unstructured networks which consist of a number of segments connected through randomly distributed nodes.