Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 10,000 papers for “Approximation algorithm”

An approximation algorithm for square packing

Stee, Rob · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2004

We consider the problem of packing squares into bins which are unit squares, where the goal is to minimize the number of bins used. We present an algorithm for this problem with an absolute worst-case ratio of 2, which is optimal provided P != NP.

Cited by 0Open access

Scalable Approximation Algorithm for Network Immunization

Juvaria Tariq, Muhammad Ahmad, Imdadullah Khan et al. · arXiv (Cornell University) · 2017

The problem of identifying important players in a given network is of pivotal importance for viral marketing, public health management, network security and various other fields of social network analysis. In this work we find the most important vertices in a graph G = (V,E) to immunize so as the chances of an epidemic outbreak is minimized. This problem is directly relevant to minimizing the impact of a contagion spread (e.g. flu virus, computer virus and rumor) in a graph (e.g. social network, computer network) with a limited budget (e.g. the number of available vaccines, antivirus software, filters). It is well known that this problem is computationally intractable (it is NP-hard). In this work we reformulate the problem as a budgeted combinational optimization problem and use techniques from spectral graph theory to design an efficient greedy algorithm to find a subset of vertices to be immunized. We show that our algorithm takes less time compared to the state of the art algorithm. Thus our algorithm is scalable to networks of much larger sizes than best known solutions proposed earlier. We also give analytical bounds on the quality of our algorithm. Furthermore, we evaluate the efficacy of our algorithm on a number of real world networks and demonstrate that the empirical performance of algorithm supplements the theoretical bounds we present, both in terms of approximation guarantees and computational efficiency.

Cited by 2Open access

Approximation Algorithm for Sparsest k-Partitioning

Anand Louis, Konstantin Makarychev · arXiv (Cornell University) · 2013

Given a graph $G$, the sparsest-cut problem asks to find the set of vertices $S$ which has the least expansion defined as $$ϕ_G(S) := \frac{w(E(S,\bar{S}))}{\min \set{w(S), w(\bar{S})}}, $$ where $w$ is the total edge weight of a subset. Here we study the natural generalization of this problem: given an integer $k$, compute a $k$-partition $\set{P_1, \ldots, P_k}$ of the vertex set so as to minimize $$ ϕ_k(\set{P_1, \ldots, P_k}) := \max_i ϕ_G(P_i). $$ Our main result is a polynomial time bi-criteria approximation algorithm which outputs a $(1 - \e)k$-partition of the vertex set such that each piece has expansion at most $O_{\varepsilon}(\sqrt{\log n \log k})$ times $OPT$. We also study balanced versions of this problem.

Cited by 2Open access

Fast Approximation Based Combinatorial Optimization Algorithm

Harsimran Kaur Er Neetu Gupta · Journal of Electrical & Electronic Systems · 2014

Abstract- Label cost optimization proposes a new improvement in label cost function, improving existing moves of α-expansion algorithm and introducing some new moves for this algorithm. In order to study the performance comparison, different metrics of energy minimization has been considered. An appropriate comparison has been drawn among proposed technique i.e. fast approximation algorithm and previous well known techniques. The objective is to effectively optimize energies so that satisfactory image segmentation can be obtained (represented with different labels respective to different objects). New combinatorial optimization algorithm have been proposed which shows promising experimental results with the new moves, which we believe could be used in any context where α-expansions are currently employed

Cited by 0Open access

An approximation algorithm for zero forcing

Ben Cameron, Jeannette Janssen, Rogers Matthew et al. · arXiv (Cornell University) · 2024

We give an algorithm that finds a zero forcing set which approximates the optimal size by a factor of $\text{pw}(G)+1$, where $\text{pw}(G)$ is the pathwidth of $G$. Starting from a path decomposition, the algorithm runs in $O(nm)$ time, where $n$ and $m$ are the order and size of the graph, respectively. As a corollary, we obtain a new upper bound on the zero forcing number in terms of the fort number and the pathwidth. The algorithm is based on a correspondence between zero forcing sets and forcing arc sets. This correspondence leads to a new bound on the zero forcing number in terms of vertex cuts, and to new, short proofs for known bounds on the zero forcing number.

Cited by 0Open access

An approximation algorithm for manhattan routing

Brenda S. Baker, Sandeep Bhatt, Frank Thomson Leighton · 1983

A linear-time approximation algorithm for routing multipoint net channels is presented. The algorithm uses at most a constant factor times the optimal number of tracks required. The notion of channel fluxis introduced and shown, like channel density, to be a lower bound for channel width. Every multipoint net channel having density d and flux f is routed within 2d+O(f) tracks, and every two-point net channel within d+O(f) tracks. Since the flux never exceeds θ(@@@@n), this proves a conjecture of Brown and Rivest [6] that every n-net channel can be routed in O(d+@@@@n) tracks.

Cited by 39

Performance of the greedy approximation algorithm.

Virgile Andreani (17087764), Eric J. South (12648421), Mary J. Dunlop (463579) · Figshare · 2024

<p>We plotted the number of binding sites that the approximation algorithm managed to fit into a sequence of a given length, <i>L</i>, normalized by the optimal solution. We repeated each scenario 10 times with random binding sites of uniform random lengths between 5 and 15 base pairs. Shaded regions represent the bootstrapped 95% confidence interval around the mean.</p> <p>(TIF)</p>

Cited by 0Open access

An Approximation Algorithm for #k-SAT

Marc Thurley · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2011

We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #k-SAT for any k>=3 within a running time that is not only non-trivial, but also significantly better than that of the currently fastest exact algorithms for the problem. More precisely, our algorithm is a randomized approximation scheme whose running time depends polynomially on the error tolerance and is mildly exponential in the number n of variables of the input formula. For example, even stipulating sub-exponentially small error tolerance, the number of solutions to 3-CNF input formulas can be approximated in time O(1.5366^n). For 4-CNF input the bound increases to O(1.6155^n). We further show how to obtain upper and lower bounds on the number of solutions to a CNF formula in a controllable way. Relaxing the requirements on the quality of the approximation, on k-CNF input we obtain significantly reduced running times in comparison to the above bounds.

Cited by 6Open access

An Efficient Multistep Stochastic Approximation Algorithm

Matthew I. Koch, James C. Spall · 1986

This paper presents an efficient and easily implemented stochastic approximation algorithm. The procedure is based on the reprocessing of input data for several steps (iterations) of the algorithm and is especially suited to the case where the input data are expensive to obtain. We show that this multistep algorithm has the usual a.s. convergence property of the standard Robbins-Monro algorithm. We also present some preliminary results on choosing the optimal number of steps for use in such data reprocessing and ilustrate the results with two numerical studies.

Cited by 2

A New Efficient Algorithm for Approximation

Lias K. Slaski, Murali Rangaswamy · 1997

Abstract : Classical radar signal processing techniques assume that the signal interference is Gaussian in nature. However, it has been shown that this interference or clutter is not always Gaussian. When non-Gaussian clutter exists, other signal processing techniques which are optimal, or more robust in non-Gaussian clutter may be more effective than the classical techniques. This requires determination of the clutter characteristics for each clutter region and then applying the appropriate signal processing technique to the data ideally in real time. In order to achieve real time it is necessary to determine this approximate Probability Density Function (PDF) using small sample data set sizes. However, until the development of the Ozturk Algorithm, there has not existed an efficient algorithm to determine an approximate PDF for a small clutter data sample set. The Ozturk Algorithm is a new statistical algorithm capable of approximating the PDF of a set of random data using on the order of 100 sample points, whereas classical techniques typically require thousands of samples. It consists of two parts, a goodness of fit test and the PDF Approximation. The goodness of fit test determines whether a sample data set is statistically consistent with a given PDF. The PDF Approximation selects the best approximate PDF from a variety of PDFs and is simply an extension of the goodness of fit test. This report describes the Ozturk Algorithm and shows an application of the algorithm to some temporal L-band radar clutter data.

Cited by 1