ALIO/EURO V conference on combinatorial optimization
ALIO/EURO V Conference on Combinatorial Optimization (ENST, Paris, 26–28 October 2005)
An Algorithm for Finding a Cycle of Fields in a Matrix
An Algorithm for M Asymmetric Travelling Salesman Problem on a Bandwidth-Limited Graph
An easy proof of the limit in the random assignment problem.
An exact method for the 2D guillotine strip packing problem.
An extreme point theorem for ordered polymatroids on chain orders.
An iterative algorithm for computing the cycle mean of a Toeplitz matrix in special form
The paper presents an iterative algorithm for computing the maximum cycle mean (or eigenvalue) of triangular Toeplitz matrix in max-plus algebra. The problem is solved by an iterative algorithm which is applied to special cycles. These cycles of triangular Toeplitz matrices are characterized by sub-partitions of .
Analysis of a near-metric TSP approximation algorithm
The traveling salesman problem (TSP) is one of the most fundamental optimization problems. We consider the β-metric traveling salesman problem (Δβ-TSP), i.e., the TSP restricted to graphs satisfying the β-triangle inequality c({v,w}) ≤ β(c({v,u}) + c({u,w})), for some cost function c and any three vertices u,v,w. The well-known path matching Christofides algorithm (PMCA) guarantees an approximation ratio of 3β2/2 and is the best known algorithm for the Δβ-TSP, for 1 ≤ β ≤ 2. We provide a complete...
Analysis of the best-worst ant system and its variants on the TSP.
In this contribution, we will study the influence of the three main components of Best-Worst Ant System: the best-worst pheromone trail update rule, the pheromone trail mutation and the restart. Both the importance of each of them and the fact whether all of them are necessary will be analyzed. The performance of different variants of this algorithm will be tested when solving different instances of the TSP.
Applications of a Special Polynomial Class of Tsp
Applications of relaxed submodularity.
Approximation algorithms for metric tree cover and generalized tour and tree covers
Given a weighted undirected graph G = (V,E), a tree (respectively tour) cover of an edge-weighted graph is a set of edges which forms a tree (resp. closed walk) and covers every other edge in the graph. The tree (resp. tour) cover problem is of finding a minimum weight tree (resp. tour) cover of G. Arkin, Halldórsson and Hassin (1993) give approximation algorithms with factors respectively 3.5 and 5.5. Later Könemann, Konjevod, Parekh, and Sinha (2003) study the linear programming relaxations...
Approximation Results Toward Nearest Neighbor Heuristic
Asymptotic differential approximation ratio : definitions, motivations and application to some combinatorial problems
Asymptotic differential approximation ratio: Definitions, motivations and application to some combinatorial problems
We first motivate and define a notion of asymptotic differential approximation ratio. For this, we introduce a new class of problems called radial problems including in particular the hereditary ones. Next, we validate the definition of the asymptotic differential approximation ratio by proving positive, conditional and negative approximation results for some combinatorial problems. We first derive a differential approximation analysis of a classical greedy algorithm for bin packing, the “first...
Balancing the stations of a self service “bike hire” system
This paper is motivated by operating self service transport systems that flourish nowadays. In cities where such systems have been set up with bikes, trucks travel to maintain a suitable number of bikes per station. It is natural to study a version of the C-delivery TSP defined by Chalasani and Motwani in which, unlike their definition, C is part of the input: each vertex v of a graph G=(V,E) has a certain amount xv of a commodity and wishes to have an amount equal to yv (we assume that and all quantities...
Balancing the stations of a self service “bike hire” system
This paper is motivated by operating self service transport systems that flourish nowadays. In cities where such systems have been set up with bikes, trucks travel to maintain a suitable number of bikes per station. It is natural to study a version of the C-delivery TSP defined by Chalasani and Motwani in which, unlike their definition, C is part of the input: each vertex v of a graph G=(V,E) has a certain amount xv of a commodity and wishes to have an amount equal to yv (we assume that and all quantities...
Bi-directional nearness in a network by AHP (Analytic Hierarchy Process) and ANP (Analytic Network Process)
Bi-directional nearness in a network by AHP (Analytic Hierarchy Process) and ANP (Analytic Network Process)
In this paper we study bi-directional nearness in a network based on AHP (Analytic Hierarchy Process) and ANP (Analytic Network Process). Usually we use forward (one-dimensional) direction nearness based on Euclidean distance. Even if the nearest point to i is point j, the nearest point to j is not necessarily point i. Sowe propose the concept of bi-directional nearness defined by AHP'ssynthesizing of weights “for” direction and “from” direction. This concept of distance is a relative distance...