Related papers: Local Search for Max-Sum Diversification
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…
This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm with the Cross-Entropy (CE) method for non smooth constrained optimization. The CE method is used as a Search step by the MADS algorithm. The result of…
The sum of radii problem ($k$-MSR) asks, given a metric space on $n$ points, to place $k$ balls covering all points so as to minimize the sum of their radii. Despite extensive study from the perspectives of approximation and parameterized…
Given a large network and a query node, finding its top-k similar nodes is a primitive operation in many graph-based applications. Recently enhancing search results with diversification have received much attention. In this paper, we…
Knapsack and Subset Sum are fundamental NP-hard problems in combinatorial optimization. Recently there has been a growing interest in understanding the best possible pseudopolynomial running times for these problems with respect to various…
In this paper we consider the classical maximum set packing problem where set cardinality is upper bounded by $k$. We show how to design a variant of a polynomial-time local search algorithm with performance guarantee $(k+2)/3$. This local…
We consider computationally expensive blackbox optimization problems and present a method that employs surrogate models and concurrent computing at the search step of the mesh adaptive direct search (MADS) algorithm. Specifically, we solve…
We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…
Parameterized local search combines classic local search heuristics with the paradigm of parameterized algorithmics. While most local search algorithms aim to improve given solutions by performing one single operation on a given solution,…
Given a set $P$ of $n$ points in $\mathbf{R}^d$, and a positive integer $k \leq n$, the $k$-dispersion problem is that of selecting $k$ of the given points so that the minimum inter-point distance among them is maximized (under Euclidean…
The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…
We study the k nearest neighbors problem in the plane for general, convex, pairwise disjoint sites of constant description complexity such as line segments, disks, and quadrilaterals and with respect to a general family of distance…
This paper proposes a new general technique for maximal subgraph enumeration which we call proximity search, whose aim is to design efficient enumeration algorithms for problems that could not be solved by existing frameworks. To support…
We consider the budgeted matroid independent set problem. The input is a ground set, where each element has a cost and a non-negative profit, along with a matroid over the elements and a budget. The goal is to select a subset of elements…
We propose a unifying framework for smoothed analysis of combinatorial local optimization problems, and show how a diverse selection of problems within the complexity class PLS can be cast within this model. This abstraction allows us to…
This paper derives polynomial-time approximation schemes for several NP-hard stochastic optimization problems from the algorithmic mechanism design and operations research literatures. The problems we consider involve a principal or seller…
MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network, given evidence. Unlike computing marginals, posteriors, and MPE (a special case of MAP), the time and space complexity of MAP is not…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
Local search is an effective method for solving large-scale combinatorial optimization problems, and it has made remarkable progress in recent years through several subtle mechanisms. In this paper, we found two ways to improve the local…
What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude $1/\epsilon^c$ is an approximation scheme for the following problems in the Euclidian…