ACM Transactions on Algorithms

In this article, we present improved inapproximability results for the k-level uncapacitated facility location problem. In particular, we show that there is no polynomial time approximation algorithm with performance guarantee better than 1.539 unless P ...

Recently, Raghavendra and Tan (SODA 2012) gave a 0.85-approximation algorithm for the Max Bisection problem. We improve their algorithm to a 0.8776-approximation. As Max Bisection is hard to approximate within α_GW + ε ≈ 0.8786 under the Unique Games ...

Nearest-neighbor search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has a wide range of applications. In many of them, such as sensor databases, location-...

This article explores the asymptotic complexity of two problems related to the Miller-Rabin-Selfridge primality test. The first problem is to tabulate strong pseudoprimes to a single fixed base a. It is now proven that tabulating up to x requires O(x) ...

In the maximum edge-disjoint paths problem, we are given a graph and a collection of pairs of vertices, and the objective is to find the maximum number of pairs that can be routed by edge-disjoint paths. An r-approximation algorithm for this problem is ...

This article studies the set cover problem under the semi-streaming model. The underlying set system is formalized in terms of a hypergraph G = (V, E) whose edges arrive one by one, and the goal is to construct an edge cover F⊆E with the objective of ...

In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a one-time instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments and must decide ...

Multi-Pivot Quicksort refers to variants of classical quicksort where in the partitioning step k pivots are used to split the input into k + 1 segments. For many years, multi-pivot quicksort was regarded as impractical, but in 2009 a two-pivot approach ...

Edge and vertex connectivity are fundamental concepts in graph theory. While they have been thoroughly studied in the case of undirected graphs, surprisingly, not much has been investigated for directed graphs. In this article, we study 2-edge ...

2-Opt is a simple local search heuristic for the traveling salesperson problem that performs very well in experiments with respect to both running time and solution quality. In contrast to this, there are instances on which 2-Opt may need an exponential ...

A fault-tolerant structure for a network is required for continued functioning following the failure of some of the network’s edges or vertices. This article considers breadth-first search (BFS) spanning trees and addresses the problem of designing a ...

We consider the classic problem of envy-free division of a heterogeneous good (“cake”) among several agents. It is known that, when the allotted pieces must be connected, the problem cannot be solved by a finite algorithm for three or more agents. The ...

We study the Minimum Latency Submodular Cover (MLSC) problem, which consists of a metric (V, d) with source r ∈ V and m monotone submodular functions f₁, f₂, …, f_m: 2^V → [0, 1]. The goal is to find a path originating at r that minimizes the total “cover ...

We introduce the st-cut version of the sparsest-cut problem, where the goal is to find a cut of minimum sparsity in a graph G(V, E) among those separating two distinguished vertices s, t ∈ V. Clearly, this problem is at least as hard as the usual (non-...

We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitive-ratio approximation schemes. Such a scheme algorithmically constructs an online algorithm with a competitive ratio arbitrarily close ...

We consider the hub label optimization problem, which arises in designing fast preprocessing-based shortest-path algorithms. We give O(log n)-approximation algorithms for the objectives of minimizing the maximum label size (ℓ_∞-norm) and simultaneously ...

The Lopsided Lovász Local Lemma (LLLL) is a powerful probabilistic principle that has been used in a variety of combinatorial constructions. While this principle began as a general statement about probability spaces, it has recently been transformed ...