arXiv subjects

Fatemeh Rajabi-Alni

Publications and source records attributed to Fatemeh Rajabi-Alni.

11 recordsLinked to original sources

arXiv2025

An $O(n^3)$ time algorithm for the maximum-weight limited-capacity many-to-many matching

Given an undirected bipartite graph $G=(A \cup B, E)$, a many-to-many matching (MM) in $G$ matches each vertex $v$ in $A$ (resp. $B$) to at least one vertex in $B$ (resp. $A$). In this paper, we consider the limited-capacity many-to-many matching (LCMM) in $G$, where each vertex $v\in A\cup B$ is matched to at least one and at most $Cap(v)$ vertices; the function $Cap : A\cup B \rightarrow \mathbb{Z}> 0$ denotes the capacity of $v$ (an upper bound on its degree in the LCMM). We give an $O(n^3)$ time algorithm for finding a maximum (respectively minimum) weight LCMM in $G$ with non-positive real (respectively non-negative real) edge weights, where $\lvert A \rvert+\lvert B \rvert=n$.

cs.DS↗

arXiv2025

Efficient Many-To-Many Matching of Points with Demands in One Dimension

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 to at least a given number of the points of $T$ (respectively $S$). We propose the first $O\left(n^2\right)$-time algorithm for computing a one dimensional MMD (OMMD) of minimum cost between $S$ and $T$, where $\left|S\right|+\left|T\right|=n$. In an OMMD problem, the input point sets $S$ and $T$ lie on the real line and the cost of matching a point to another point equals the Euclidean distance between the two points. We also study a generalized version of the MMD problem, the many-to-many matching with demands and capacities (MMDC) problem, that in which each point has a limited capacity in addition to a demand. We give the first $O(n^2)$-time algorithm for the minimum-cost one dimensional MMDC (OMMDC) problem.

cs.CG↗

arXiv2024

Approximation Algorithms for the Freeze Tag Problem inside Polygons

The freeze tag problem (FTP) aims to awaken a swarm of robots with one or more initial awake robots as soon as possible. Each awake robot must touch a sleeping robot to wake it up. Once a robot is awakened, it can assist in awakening other sleeping robots. We study this problem inside a polygonal domain and present approximation algorithms for it.

cs.CG↗

arXiv2023

A faster algorithm for the limited-capacity many-to-many point matching in one dimension

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 capacity of p. In this paper, we present the first linear time algorithm for finding a minimum-cost one-dimensional LCMM (OLCMM) between S and T, where S and T are points lying on a line, and the cost of matching p in S to q in T equals the l_2 distance between p,q. Our algorithm improves the previous best-known quadratic time algorithm.

cs.CG↗

arXiv2022

Computing a many-to-many matching with demands and capacities between two sets using the Hungarian algorithm

Given two sets A={a_1,a_2,...,a_s} and {b_1,b_2,...,b_t}, a many-to-many matching with demands and capacities (MMDC) between A and B matches each element a_i in A to at least α_i and at most α'_i elements in B, and each element b_j in B to at least β_j and at most β'_j elements in A for all 1=<i<=s and 1=<j<=t. In this paper, we present an algorithm for finding a minimum-cost MMDC between A and B using the well-known Hungarian algorithm.

cs.DS↗

arXiv2018

An O(n^2) algorithm for Many-To-Many Matching of Points with Demands in One Dimension

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(n^2)time algorithm for computing an OMMD between S and T, where |S| + |T| = n.

cs.DS↗

arXiv2013

Embedding a balanced binary tree on a bounded point set

Given an undirected planar graph G with n vertices and a set S of n points inside a simple polygon P, a point-set embedding of G on S is a planar drawing of G such that each vertex is mapped to a distinct point of S and the edges are polygonal chains surrounded by P. A special case of the embedding problem is that in which G is a balanced binary tree. In this paper, we present a new algorithm for embedding an n-vertex balanced binary tree BBT on a set S of n points bounded by a simple m-gon P in O(m^2 + n(log n)^2 + mn) time with at most O(m) bends per edge.

cs.CG↗

arXiv2013

Two exact algorithms for the generalized assignment problem

Let A={a_1,a_2,...,a_s} and B={b_1,b_2,...,b_t} be two sets of objects with s+r=n, the generalized assignment problem assigns each element a_i in A to at least alpha_i and at most alpha '_i elements in B, and each element b_j in B to at least beta_j and at most beta '_j elements in A for all 1 <= i <= s and 1 <= j <= t. In this paper, we present an O(n^4) time and O(n) space algorithm for this problem using the well known Hungarian algorithm. We also present an O(n^3) algorithm for a special case of the generalized assignment, called the limited-capacity assignment problem, where alpha_i,beta_j=1 for all i,j.

cs.DS↗

arXiv2013

A new algorithm for Many to Many Matching with Demands and Capacities

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 beta_j and at most beta_j points in A for all 1 <= i <= s and 1 <= j <= t. In this paper, we present an O(n^4) time and O(n) space algorithm for this problem.

cs.DS↗

arXiv2013

Many 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 in A to at least alpha'i and at most alphai points in B, and each point bj in B to at least betaj and at most beta'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.

cs.DS↗

arXiv2012

Limited-Capacity Many-To-Many Point Matching in One Dimension

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 matching problem, where the number of points that can be matched to each point, that is the capacity of each point, is limited. In this paper, we provide an O(n^2) time algorithm for the one dimensional minimum-cost limited capacity many-to-many matching problem, where |S| + |T| = n. Our algorithm improves the best previous time complexity of O(k(n^2)), that in which k is the largest capacity of the points in the union of S and T. In this problem, both S and T lie on the real line and the cost of matching s in S to t in T is equal to the distance between s and t.

cs.CG↗