Related papers: Dynamic Geometric Independent Set
Independent set is a fundamental problem in combinatorial optimization. While in general graphs the problem is essentially inapproximable, for many important graph classes there are approximation algorithms known in the offline setting.…
A fundamental question is whether one can maintain a maximum independent set in polylogarithmic update time for a dynamic collection of geometric objects in Euclidean space. Already, for a set of intervals, it is known that no dynamic…
We consider the problem of maintaining an approximate maximum independent set of geometric objects under insertions and deletions. We present data structures that maintain a constant-factor approximate maximum independent set for broad…
Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of…
Map labeling is a classical problem in cartography and geographic information systems (GIS) that asks to place labels for area, line, and point features, with the goal to select and place the maximum number of independent, i.e.,…
We present the first algorithm for maintaining a maximal independent set (MIS) of a fully dynamic graph---which undergoes both edge insertions and deletions---in polylogarithmic time. Our algorithm is randomized and, per update, takes…
We study the maximum geometric independent set and clique problems in the streaming model. Given a collection of geometric objects arriving in an insertion only stream, the aim is to find a subset such that all objects in the subset are…
We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local search algorithm yields a \PTAS. For the weighted case,…
In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees. In particular, we obtain improved dynamic algorithms that, given an unweighted and…
We study the Maximum Independent Set problem for geometric objects given in the data stream model. A set of geometric objects is said to be independent if the objects are pairwise disjoint. We consider geometric objects in one and two…
We develop simple and general techniques to obtain faster (near-linear time) static approximation algorithms, as well as efficient dynamic data structures, for four fundamental geometric optimization problems: minimum piercing set (MPS),…
In the maximum independent set of convex polygons problem, we are given a set of $n$ convex polygons in the plane with the objective of selecting a maximum cardinality subset of non-overlapping polygons. Here we study a special case of the…
In the Maximum Independent Set of Hyperrectangles problem, we are given a set of $n$ (possibly overlapping) $d$-dimensional axis-aligned hyperrectangles, and the goal is to find a subset of non-overlapping hyperrectangles of maximum…
We investigate dynamic versions of geometric set cover and hitting set where points and ranges may be inserted or deleted, and we want to efficiently maintain an (approximately) optimal solution for the current problem instance. While their…
Geometric set cover is a classical problem in computational geometry, which has been extensively studied in the past. In the dynamic version of the problem, points and ranges may be inserted and deleted, and our goal is to efficiently…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
In this work, we study two fundamental graph optimization problems, minimum vertex cover (MVC) and maximum-cardinality matching (MCM), for intersection graphs of geometric objects, e.g., disks, rectangles, hypercubes, etc., in…
We develop the first theoretically-efficient algorithm for maintaining the maximal independent set (MIS) of a graph in the parallel batch-dynamic setting. In this setting, a graph is updated with batches of edge insertions/deletions, and…
A maximal independent set (MIS) can be maintained in an evolving $m$-edge graph by simply recomputing it from scratch in $O(m)$ time after each update. But can it be maintained in time sublinear in $m$ in fully dynamic graphs? We answer…
Maximum independent set from a given set $D$ of unit disks intersecting a horizontal line can be solved in $O(n^2)$ time and $O(n^2)$ space. As a corollary, we design a factor 2 approximation algorithm for the maximum independent set…