An O(n^2) algorithm for Many-To-Many Matching of Points with Demands in One Dimension
نویسندگان
چکیده
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 number of the points of the other set (each point has a demand). In this paper we consider a special case of MMD problem, the one-dimensional MMD (OMMD), where the input point sets S and T lie on the line. That is, the cost of matching a pair of points is equal to the distance between the two points. we present the first O (
منابع مشابه
A new algorithm for Many to Many Matching with Demands and Capacities
Let A = {a1, a2, . . . , as} and {b1, b2, . . . , bt} with s+r = n, the many to many point matching with demands and capacities matches each point ai ∈ A to at least αi and at most α ′ i points in B, and each point bj ∈ B to at least βj and at most β ′j points in A for all 1 ≤ i ≤ s and 1 ≤ j ≤ t. In this paper, we present an O(n) time and O(n) space algorithm for this problem.
متن کاملSweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملEfficient Approximation Algorithms for Point-set Diameter in Higher Dimensions
We study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...
متن کاملتعبیه ی هندسی درخت درنقاط داخل یک چندضلعی با حداقل تعداد خم
In this paper we consider to embed a tree T with N vertices on a set of N points inside a simple polygon on n vertices and the goal is to minimize the number of bends. The main idea of our algorithm is modeling the problem into graph matching problem and uses the graph matching algorithms. We apply the concept of error-correction transformation and find the appropriate cost function then we per...
متن کاملMany to Many Matching with Demands and Capacities
Let A and B be two finite sets of points with total cardinality n, the many to many point matching with demands and capacities matches each point ai ∈ A to at least αi and at most α ′ i points in B, and each point bj ∈ B to at least βj and at most β ′ j points in A for all 1 ≤ i ≤ s and 1 ≤ j ≤ t. In this paper, we present an upper bound for this problem using our new polynomial time algorithm.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1702.01083 شماره
صفحات -
تاریخ انتشار 2017