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On the Two-Dimensional Knapsack Problem for Convex Polygons
ACM Transactions on Algorithms (TALG), Volume 20, Issue 2Article No.: 16, Pages 1–38https://doi.org/10.1145/3644390We study the two-dimensional geometric knapsack problem for convex polygons. Given a set of weighted convex polygons and a square knapsack, the goal is to select the most profitable subset of the given polygons that fits non-overlappingly into the ...
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- research-articleMarch 2024
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- research-articleSeptember 2023
- research-articleMarch 2023
A PTAS for Capacitated Vehicle Routing on Trees
ACM Transactions on Algorithms (TALG), Volume 19, Issue 2Article No.: 17, Pages 1–28https://doi.org/10.1145/3575799We give a polynomial time approximation scheme (PTAS) for the unit demand capacitated vehicle routing problem (CVRP) on trees, for the entire range of the tour capacity. The result extends to the splittable CVRP.
- research-articleMarch 2023
Approximation Schemes for Capacitated Vehicle Routing on Graphs of Bounded Treewidth, Bounded Doubling, or Highway Dimension
ACM Transactions on Algorithms (TALG), Volume 19, Issue 2Article No.: 20, Pages 1–36https://doi.org/10.1145/3582500In this article, we present Approximation Schemes for Capacitated Vehicle Routing Problem (CVRP) on several classes of graphs. In CVRP, introduced by Dantzig and Ramser in 1959 [14], we are given a graph G=(V,E) with metric edges costs, a depot r ∈ V, and ...
- research-articleMarch 2023
Universal Algorithms for Clustering Problems
ACM Transactions on Algorithms (TALG), Volume 19, Issue 2Article No.: 15, Pages 1–46https://doi.org/10.1145/3572840This article presents universal algorithms for clustering problems, including the widely studied k-median, k-means, and k-center objectives. The input is a metric space containing all potential client locations. The algorithm must select k cluster centers ...
- research-articleFebruary 2023
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- research-articleOctober 2022
Network Design for s-t Effective Resistance
ACM Transactions on Algorithms (TALG), Volume 18, Issue 3Article No.: 22, Pages 1–45https://doi.org/10.1145/3522588We consider a new problem of designing a network with small s-t effective resistance. In this problem, we are given an undirected graph G = (V,E), two designated vertices s,t ∈ V, and a budget k. The goal is to choose a subgraph of G with at most k edges ...
- research-articleOctober 2022
Tolerant Testers of Image Properties
ACM Transactions on Algorithms (TALG), Volume 18, Issue 4Article No.: 37, Pages 1–39https://doi.org/10.1145/3531527We initiate a systematic study of tolerant testers of image properties or, equivalently, algorithms that approximate the distance from a given image to the desired property. Image processing is a particularly compelling area of applications for sublinear-...
- research-articleOctober 2022
Sticky Brownian Rounding and its Applications to Constraint Satisfaction Problems
ACM Transactions on Algorithms (TALG), Volume 18, Issue 4Article No.: 33, Pages 1–50https://doi.org/10.1145/3459096Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson [31] has been extensively studied ...
- research-articleOctober 2021
Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem
ACM Transactions on Algorithms (TALG), Volume 17, Issue 4Article No.: 35, Pages 1–12https://doi.org/10.1145/3478537We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum-...
- research-articleOctober 2021
Approximating Geometric Knapsack via L-packings
ACM Transactions on Algorithms (TALG), Volume 17, Issue 4Article No.: 33, Pages 1–67https://doi.org/10.1145/3473713We study the two-dimensional geometric knapsack problem, in which we are given a set of n axis-aligned rectangular items, each one with an associated profit, and an axis-aligned square knapsack. The goal is to find a (non-overlapping) packing of a maximum ...
- research-articleJuly 2021
The Quest for Strong Inapproximability Results with Perfect Completeness
ACM Transactions on Algorithms (TALG), Volume 17, Issue 3Article No.: 27, Pages 1–35https://doi.org/10.1145/3459668The Unique Games Conjecture has pinned down the approximability of all constraint satisfaction problems (CSPs), showing that a natural semidefinite programming relaxation offers the optimal worst-case approximation ratio for any CSP. This elegant ...
- research-articleJuly 2021
The Complexity of Approximately Counting Retractions to Square-free Graphs
ACM Transactions on Algorithms (TALG), Volume 17, Issue 3Article No.: 22, Pages 1–51https://doi.org/10.1145/3458040A retraction is a homomorphism from a graph G to an induced subgraph H of G that is the identity on H. In a long line of research, retractions have been studied under various algorithmic settings. Recently, the problem of approximately counting ...