Related papers: Exact and Approximation Algorithms for Many-To-Man…

In this paper, we study the many-to-many matching problem on planar point sets with integer coordinates: Given two disjoint sets $R,B \subset [\Delta]^2$ with $|R|+|B|=n$, the goal is to select a set of edges between $R$ and $B$ so that…

Geometric matching is an important topic in computational geometry and has been extensively studied over decades. In this paper, we study a geometric-matching problem, known as geometric many-to-many matching. In this problem, the input is…

Given two point sets S and T, in a many-to-many matching between S and T each point in S is assigned to one or more points in T and vice versa. A generalization of the many-to-many matching problem is the limited capacity many-to-many…

Let $A$ and $B$ be two point sets in the plane of sizes $r$ and $n$ respectively (assume $r \leq n$), and let $k$ be a parameter. A matching between $A$ and $B$ is a family of pairs in $A \times B$ so that any point of $A \cup B$ appears in…

Given two point sets S and T, we study the many-to-many matching with demands problem (MMD problem) which is a generalization of the many-to-many matching problem (MM problem). In an MMD, each point of one set must be matched to a given…

Given two point sets $S$ and $T$, the minimum-cost many-to-many matching with demands (MMD) problem is the problem of finding a minimum-cost many-to-many matching between $S$ and $T$ such that each point of $S$ (respectively $T$) is matched…

A bottleneck plane perfect matching of a set of $n$ points in $\mathbb{R}^2$ is defined to be a perfect non-crossing matching that minimizes the length of the longest edge; the length of this longest edge is known as {\em bottleneck}. The…

In the Maximum Independent Set of Objects problem, we are given an $n$-vertex planar graph $G$ and a family $\mathcal{D}$ of $N$ objects, where each object is a connected subgraph of $G$. The task is to find a subfamily $\mathcal{F}…

We study the Euclidean minimum weight perfect matching problem for $n$ points in the plane. It is known that any deterministic approximation algorithm whose approximation ratio depends only on $n$ requires at least $\Omega(n \log n)$ time.…

We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of $n$ items and that the available workspace is $\Theta(s)$ bits, where $\lg n \leq s \leq n…

We consider the problem of tracking $n$ targets in the plane using $2n$ cameras. We can use two cameras to estimate the location of a target. We are then interested in forming $n$ camera pairs where each camera belongs to exactly one pair,…

We study a fundamental problem in Computational Geometry, the planar two-center problem. In this problem, the input is a set $S$ of $n$ points in the plane and the goal is to find two smallest congruent disks whose union contains all points…

It is well-known that every $n$-vertex planar graph with minimum degree 3 has a matching of size at least $\frac{n}{3}$. But all proofs of this use the Tutte-Berge-formula for the size of a maximum matching. Hence these proofs are not…

We consider a bichromatic two-center problem for pairs of points. Given a set $S$ of $n$ pairs of points in the plane, for every pair, we want to assign a red color to one point and a blue color to the other, in such a way that the value…

Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…

In 1991, Edelsbrunner and Tan gave an O(n^2) algorithm for finding the MinMax Length triangulation of a set of points in the plane. In this paper we resolve one of the open problems stated in that paper, by showing that finding a MaxMin…

We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a * b rectangles such that the sum of the weights of the points in P…

Let A={a_1,a_2,...,a_s} and {b_1,b_2,...,b_t} with s+r=n, the many to many point matching with demands and capacities matches each point a_i in A to at least alpha_i and at most alpha_i points in B, and each point b_j in B to at least…

Given two sets S and T, a limited-capacity many-to-many matching (LCMM) between S and T matches each element p in S (resp. T) to at least 1 and at most Cap(p) elements in T (resp. S), where the function Cap:S\cup T-> Z>0 denotes the…

Let $P$ be a set of at most $n$ points and let $R$ be a set of at most $n$ geometric ranges, such as for example disks or rectangles, where each $p \in P$ has an associated supply $s_{p} > 0$, and each $r \in R$ has an associated demand…