Search results for "Greedy algorithm"
showing 10 items of 26 documents
Whom to befriend to influence people
2020
Alice wants to join a new social network, and influence its members to adopt a new product or idea. Each person $v$ in the network has a certain threshold $t(v)$ for {\em activation}, i.e adoption of the product or idea. If $v$ has at least $t(v)$ activated neighbors, then $v$ will also become activated. If Alice wants to activate the entire social network, whom should she befriend? More generally, we study the problem of finding the minimum number of links that a set of external influencers should form to people in the network, in order to activate the entire social network. This {\em Minimum Links} Problem has applications in viral marketing and the study of epidemics. Its solution can be…
Approximation Algorithms for Multicoloring Planar Graphs and Powers of Square and Triangular Meshes
2006
A multicoloring of a weighted graph G is an assignment of sets of colors to the vertices of G so that two adjacent vertices receive two disjoint sets of colors. A multicoloring problem on G is to find a multicoloring of G. In particular, we are interested in a minimum multicoloring that uses the least total number of colors. The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11/6-approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infi…
Application independent greedy particle tracking method for 3D fluorescence microscopy image series
2012
Single-particle tracking is computationally a challenging problem, and usually solved with local methods. Local methods suffer from defects in the image data or in the detection of particles, such as temporal disappearing of particles. A particle tracking method has to provide a solution also to real disappearing and appearing of particles as a result of merging and splitting. Here, we present an efficient, greedy algorithm as a solution to the particle tracking problem. This improved local method is application independent, as it has high configurability of the function used to solve particle correspondence. To demonstrate the accuracy of the method, we apply it to real microscopy image da…
A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems
2005
This paper presents a greedy randomized adaptive search procedure (GRASP) for the constrained two-dimensional non-guillotine cutting problem, the problem of cutting the rectangular pieces from a large rectangle so as to maximize the value of the pieces cut. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perform extensive computational experiments with well-known instances previously reported, first to select the best alternatives and then to compare the efficiency of our algorithm with other procedures.
A genetic algorithm for the minimum generating set problem
2016
Graphical abstractDisplay Omitted HighlightsWe propose a novel formulation for the MGS problem based on multiple knapsack.The so-conceived MGS problem is solved by a novel GA.The GA embeds an intelligent construction method and specialized crossover operators.We perform a thorough comparison with regards to state-of-the-art algorithms.The proposal proves to be very competitive, specially for large and hard instances. Given a set of positive integers S, the minimum generating set problem consists in finding a set of positive integers T with a minimum cardinality such that every element of S can be expressed as the sum of a subset of elements in T. It constitutes a natural problem in combinat…
Team Theory and Person-by-Person Optimization with Binary Decisions
2012
In this paper, we extend the notion of person-by-person (pbp) optimization to binary decision spaces. The novelty of our approach is the adaptation to a dynamic team context of notions borrowed from the pseudo-boolean optimization field as completely local-global or unimodal functions and submodularity. We also generalize the concept of pbp optimization to the case where groups of $m$ decisions makers make joint decisions sequentially, which we refer to as $m$b$m$ optimization. The main contribution is a description of sufficient conditions, verifiable in polynomial time, under which a pbp or an $m$b$m$ optimization algorithm converges to the team-optimum. As a second contribution, we prese…
Reactive GRASP for the strip-packing problem
2008
This paper presents a greedy randomized adaptive search procedure (GRASP) for the strip packing problem, which is the problem of placing a set of rectangular pieces into a strip of a given width and infinite height so as to minimize the required height. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perform extensive computational experiments with well-known instances which have been previously reported, first to select the best alternatives and then to compare the efficiency of our algorithm with other procedures. The results show that the GRASP algorithm outperforms recently reported metaheuristics.
Separating capacity constraints in the CVRP using tabu search
1998
Abstract Branch and Cut methods have shown to be very successful in the resolution of some hard combinatorial optimization problems. The success has been remarkable for the Symmetric Traveling Salesman Problem (TSP). The crucial part in the method is the cutting plane algorithm: the algorithm that looks for valid inequalities that cut off the current nonfeasible linear program (LP) solution. In turn this part relies on a good knowledge of the corresponding polyhedron and our ability to design algorithms that can identify violated valid inequalities. This paper deals with the separation of the capacity constraints for the Capacitated Vehicle Routing Problem (CVRP). Three algorithms are prese…
On Optimal Solutions for the Optimal Communication Spanning Tree Problem
2009
This paper presents an experimental investigation into the properties of the optimal communication spanning tree (OCST) problem. The OCST problem seeks a spanning tree that connects all the nodes and satisfies their communication requirements at a minimum total cost. The paper compares the properties of random trees to the properties of the best solutions for the OCST problem that are found using an evolutionary algorithm. The results show, on average, that the optimal solution and the minimum spanning tree (MST) share a higher number of links than the optimal solution and a random tree. Furthermore, optimal solutions for OCST problems with randomly chosen distance weights share a higher n…
Greedy and K-Greedy algoritmhs for multidimensional data association
2011
[EN] The multidimensional assignment (MDA) problem is a combinatorial optimization problem arising in many applications, for instance multitarget tracking (MTT). The objective of an MDA problem of dimension $d\in\Bbb{N}$ is to match groups of $d$ objects in such a way that each measurement is associated with at most one track and each track is associated with at most one measurement from each list, optimizing a certain objective function. It is well known that the MDA problem is NP-hard for $d\geq3$. In this paper five new polynomial time heuristics to solve the MDA problem arising in MTT are presented. They are all based on the semi-greedy approach introduced in earlier research. Experimen…