Related papers: On the Average-Case Performance of Greedy for Maxi…
Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved…
MapReduce has become the de facto standard model for designing distributed algorithms to process big data on a cluster. There has been considerable research on designing efficient MapReduce algorithms for clustering, graph optimization, and…
This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards)…
We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant degree regular graphs. We show that for $r$-regular graphs with $n$ nodes and girth at least $g$, the…
We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased…
In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables…
We study distributed algorithms that find a maximal matching in an anonymous, edge-coloured graph. If the edges are properly coloured with $k$ colours, there is a trivial greedy algorithm that finds a maximal matching in $k-1$ synchronous…
We study submodular maximization problems with matroid constraints, in particular, problems where the objective can be expressed via compositions of analytic and multilinear functions. We show that for functions of this form, the so-called…
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.…
We study the problem of maximizing a submodular function, subject to a cardinality constraint, with a set of agents communicating over a connected graph. We propose a distributed greedy algorithm that allows all the agents to converge to a…
We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent LP rounding algorithms and a hybrid algorithm…
We consider the MINGREEDY strategy for Maximum Cardinality Matching. MINGREEDY repeatedly selects an edge incident with a node of minimum degree. For graphs of degree at most $\Delta$ we show that MINGREEDY achieves approximation ratio at…
Setcover greedy algorithm is a natural approximation algorithm for test set problem. This paper gives a precise and tighter analysis of performance guarantee of this algorithm. The author improves the performance guarantee $2\ln n$ which…
We study sublinear time algorithms for estimating the size of maximum matching in graphs. Our main result is a $(\frac{1}{2}+\Omega(1))$-approximation algorithm which can be implemented in $O(n^{1+\epsilon})$ time, where $n$ is the number…
Nearly three decades ago, Bar-Noy, Motwani and Naor showed that no online edge-coloring algorithm can edge color a graph optimally. Indeed, their work, titled "the greedy algorithm is optimal for on-line edge coloring", shows that the…
Submodular functions are a broad class of set functions, which naturally arise in diverse areas. Many algorithms have been suggested for the maximization of these functions. Unfortunately, once the function deviates from submodularity, the…
In the design of greedy algorithms for the maximum cardinality matching problem the utilization of degree information when selecting the next edge is a well established and successful approach. We define the class of "degree sensitive"…
Given a set ${\cal R}=\{R_1,R_2,..., R_n\}$ of $n$ randomly positioned axis parallel rectangles in 2D, the problem of computing the minimum clique cover (MCC) and maximum independent set (MIS) for the intersection graph $G({\cal R})$ of the…
The standard greedy algorithm has been recently shown to enjoy approximation guarantees for constrained non-submodular nondecreasing set function maximization. While these recent results allow to better characterize the empirical success of…
In this paper we analyze the worst-case performance of a greedy algorithm called Largest-Z-ratio-First for the problem of scheduling unreliable jobs on m parallel machines. Each job is characterized by a success probability and a reward…