A Fast and Efficient algorithm for Many-To-Many Matching of Points with Demands in One Dimension

Given two point sets S and T, a 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(n^2) time algorithm for computing a one dimensional MMD (OMMD) of minimum cost between S and T, where |S|+|T| = 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 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.Comment: 14 pages,8 figures. arXiv admin note: substantial text overlap with arXiv:1702.0108

A Faster Algorithm for the Limited-Capacity Many-to-Many Point Matching in One Dimension

Given two point sets S and T on a line, we present the first linear time algorithm for finding the limited capacity many-to-many matching (LCMM) between S and T improving the previous best known quadratic time algorithm. The aim of the LCMM is to match each point of S (T) to at least one point of T (S) such that the matching costs is minimized and the number of the points matched to each point is limited to a given number.Comment: 18 pages, 7 figures. arXiv admin note: text overlap with arXiv:1702.0108

On the job rotation problem

The job rotation problem (JRP) is the following: Given an $n \times n$ matrix $A$ over \Re \cup \{\ -\infty\ \}\ and $k \leq n$, find a $k \times k$ principal submatrix of $A$ whose optimal assignment problem value is maximum. No polynomial algorithm is known for solving this problem if $k$ is an input variable. We analyse JRP and present polynomial solution methods for a number of special cases

Regularized pointwise map recovery from functional correspondence

The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point-to-point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly-isometric, and easily extends to recovering the point-to-point correspondence in part-to-whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases

Parallel Ant Colony Optimization on the University Course-Faculty Timetabling Problem in MSU-IIT Distributed Application in Erlang/OTP

The University Course-Faculty Timetabling Problem (UCFTP) occurs in the Mindanao State University-Iligan Institute of Technology (MSU-IIT) as the delegation of classrooms for available subjects including time schedule and appropriate faculty personnel, taking into consideration constraints such as classroom capacities, location, and faculty preferences, etc. It is a more difficult variant of the classical University Course Timetabling Problem, which is an assignment problem and known to be NP-hard. This paper presents parallel Ant Colony Optimization Max-Min Ant System (ACO-MMAS) algorithm as an approach in solving the UCFTP instance in the institute. ACO employs virtual ants moving across a search space and using an indirect form of constructive feedback by depositing pheromones on the paths they traverse in order to influence other ants in their searches. We have developed an application to automate the timetabling process using Erlang/OTP, a functional language specializing in concurrent and distributed systems. UCFTP was successfully represented into a mathematical problem instance and solved using the ACO-MMAS algorithm applied on a distributed network setup under Parallel Independent Run and Unidirectional Ring topologies. Extensive testing was performed to properly analyze the search behavior under different parameter settings

Computing random rr-orthogonal Latin squares

Two Latin squares of order $n$ are $r$-orthogonal if, when superimposed, there are exactly $r$ distinct ordered pairs. The spectrum of all values of $r$ for Latin squares of order $n$ is known. A Latin square $A$ of order $n$ is $r$-self-orthogonal if $A$ and its transpose are $r$-orthogonal. The spectrum of all values of $r$ is known for all orders $n\ne 14$. We develop randomized algorithms for computing pairs of $r$-orthogonal Latin squares of order $n$ and algorithms for computing $r$-self-orthogonal Latin squares of order $n$