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A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size $n$ subject to cardinality constraint $k$; the algorithm is based upon the idea of interlacing two…
$\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path…
The task of outlier detection is to find small groups of data objects that are exceptional when compared with rest large amount of data. In [38], the problem of outlier detection in categorical data is defined as an optimization problem and…
A base for a permutation group $G$ acting on a set $\Omega$ is a subset $\mathcal{B}$ of $\Omega$ whose pointwise stabiliser $G_{(\mathcal{B})}$ is trivial. There is a natural greedy algorithm for constructing a base of relatively small…
Given a graph on $n$ vertices and an integer $k$, the feedback vertex set problem asks for the deletion of at most $k$ vertices to make the graph acyclic. We show that a greedy branching algorithm, which always branches on an undecided…
Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent…
Consider the puzzle: given a number, remove $k$ digits such that the resulting number is as large as possible. Various techniques were employed to derive a linear-time solution to the puzzle: predicate logic was used to justify the…
\begin{abstract} Greedy permutations, also known as Gonzalez Orderings or Farthest Point Traversals are a standard way to approximate $k$-center clustering and have many applications in sampling and approximating metric spaces. A greedy…
The greedy defining sets of graphs were appeared first time in [M. Zaker, Greedy defining sets of graphs, Australas. J. Combin, 2001]. We show that to determine the greedy defining number of bipartite graphs is an NP-complete problem. This…
Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify…
We demonstrate that the greedy algorithm for reduction of divisors on metric graphs need not terminate by modeling the Euclidean algorithm in this context. We observe that any infinite reduction has a well defined limit allowing us to treat…
In this work, we consider the problem of steering the first two moments of the uncertain state of a discrete time nonlinear stochastic system to prescribed goal quantities at a given final time. In principle, the latter problem can be…
A sequence $S$ of vertices of a graph $G$ is called a dominating sequence of $G$ if $(i)$ each vertex $v$ of $S$ dominates a vertex of $G$ that was not dominated by any of the vertices preceding vertex $v$ in $S$, and $(ii)$ every vertex of…
The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How good is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two…
Using greedy algorithms to generate de Bruijn sequences is a classical approach that has produced numerous interesting theoretical results. This paper investigates an algorithm which we call the Generalized Prefer-Opposite (GPO). It…
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…
Kernel-based schemes are state-of-the-art techniques for learning by data. In this work we extend some ideas about kernel-based greedy algorithms to exponential-polynomial splines, whose main drawback consists in possible overfitting and…
A universal cycle for permutations of length $n$ is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length $n$, and containing all permutations of length $n$ as factors. It is well known…
The frame algorithm uses a simple recursive formula to approximate an unknown vector from its frame coefficients. This note introduces an adaptive version of the frame algorithm that maximizes the error reduction between steps in terms of…
Selecting the best set of ads is critical for advertisers for a given set of keywords, which involves the composition of ads from millions of candidates. While click through rates (CTRs) are important, there could be high correlation among…