Integer programming formulations of discrete hub location problems

Methods and problems of communication in usual networks

The study of what can be computed by a team of autonomous mobile robots, originally started in robotics and AI, has become increasingly popular in theoretical computer science (especially in distributed computing), where it is now an integral part of the investigations on computability by mobile entities. The robots are identical computational entities located and able to move in a spatial universe; they operate without explicit communication and are usually unable to remember the past; they are extremely simple, with limited resources, and individually quite weak. However, collectively the robots are capable of performing complex tasks, and form a system with desirable fault-tolerant and self-stabilizing properties. The research has been concerned with the computational aspects of such systems. In particular, the focus has been on the minimal capabilities that the robots should have in order to solve a problem. This book focuses on the recent algorithmic results in the field of distributed computing by oblivious mobile robots (unable to remember the past). After introducing the computational model with its nuances, we focus on basic coordination problems: pattern formation, gathering, scattering, leader election, as well as on dynamic tasks such as flocking. For each of these problems, we provide a snapshot of the state of the art, reviewing the existing algorithmic results. In doing so, we outline solution techniques, and we analyze the impact of the different assumptions on the robots' computability power. Table of Contents: Introduction / Computational Models / Gathering and Convergence / Pattern Formation / Scatterings and Coverings / Flocking / Other Directions

Distributed Computing by Oblivious Mobile Robots

Consider a set of $n>2$ identical mobile computational entities in the plane, called robots, operating in Look-Compute-Move cycles, without any means of direct communication. The Gathering Problem is the primitive task of all entities gathering in finite time at a point not fixed in advance, without any external control. The problem has been extensively studied in the literature under a variety of strong assumptions (e.g., synchronicity of the cycles, instantaneous movements, complete memory of the past, common coordinate system, etc.). In this paper we consider the setting without those assumptions, that is, when the entities are oblivious (i.e., they do not remember results and observations from previous cycles), disoriented (i.e., have no common coordinate system), and fully asynchronous (i.e., no assumptions exist on timing of cycles and activities within a cycle). The existing algorithmic contributions for such robots are limited to solutions for $n \leq 4$ or for restricted sets of initial configura...

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Distributed Computing by Mobile Robots: Gathering

Considerable attention in recent theoretical computer science is devoted to parallel computing. Here, we would like to present a special part of this large topic, namely, the part devoted to an abstract study of the dissemination of information in interconnection networks. The importance of this research area lies in the fact that the ability of a network to effectively disseminate information is an important qualitative measure for the suitabilty of the network for parallel computing. This follows simply from the observation that the communication among processes working in parallel is one of the main parts of the whole parallel computation. So, the effectivity of information exchange among processors essentially influences the effectivity of the whole computation process.

Dissemination of Information in Interconnection Networks (Broadcasting & Gossiping)

Gathering asynchronous oblivious mobile robots in a ring

We consider a fixed communication network where (software) agents can move freely from node to node along the edges. A black hole is a faulty or malicious node in the network such that if an agent enters this node, then it immediately “dies.” We are interested in designing an efficient communication algorithm for the agents to identify all black holes. We assume that we have k agents starting from the same node s and knowing the topology of the whole network. The agents move through the network in synchronous steps and can communicate only when they meet in a node. At the end of the exploration of the network, at least one agent must survive and must know the exact locations of the black holes. If the network has n nodes and b black holes, then any exploration algorithm needs Ω(n/k + Db) steps in the worst-case, where Db is the worst case diameter of the network with at most b nodes deleted. We give a general algorithm which completes exploration in O((n/k)logn/loglogn + bDb) steps for arbitrary networks, if b≤k/2. In the case when b≤k/2, and , we give a refined algorithm which completes exploration in asymptotically optimal O(n/k) steps.

Searching for black-hole faults in a network using multiple agents

We consider the problem of gathering identical, memoryless, mobile robots in one node of an anonymous unoriented ring. Robots start from different nodes of the ring. They operate in Look-Compute-Move cycles and have to end up in the same node. In one cycle, a robot takes a snapshot of the current configuration (Look), makes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each robot. For an odd number of robots we prove that gathering is feasible if and only if the initial configuration is not periodic, and we provide a gathering algorithm for any such configuration. For an even number of robots we decide feasibility of gathering except for one type of symmetric initial configurations, and provide gathering algorithms for initial configurations proved to be gatherable.

Gathering Asynchronous Oblivious Mobile Robots in a Ring

Towards the notion of stability of approximation for hard optimization tasks and the traveling salesman problem

The traveling salesman problem (TSP) is one of the hardest optimization problems in NPO because it does not admit any polynomial time approximation algorithm (unless P = NP). On the other hand we have a polynomial time approximation scheme (PTAS) for the Euclidean TSP and the 3/2 -approximation algorithm of Christofides for TSP instances satisfying the triangle inequality. The main contributions of this paper are the following: (i) We essentially modify the method of Engebretsen [En99] in order to get a lower bound of 3813/3812-Ɛ on the polynomial-time approximability of the metric TSP for any Ɛ > 0. This is an improvement over the lower bound of 5381/5380 -Ɛ in [En99]. Using this approach we moreover prove a lower bound δβ on the approximability of Δβ-TSP for 1/2 < β < 1, where Δβ-TSP is a subproblem of the TSP whose input instances satisfy the β-sharpened triangle inequality cost({u, v}) ≤ β ċ (cost({u, v}) + cost({x, v})) for all vertices u, v, x. (ii) We present three different methods for the design of polynomial-time approximation algorithms for Δβ-TSP with 1/2 < β < 1, where the approximation ratio lies between 1 and 3/2, depending on β.

Ralf Klasing

Papers

Gathering asynchronous oblivious mobile robots in a ring

Searching for black-hole faults in a network using multiple agents

Gathering Asynchronous Oblivious Mobile Robots in a Ring

Towards the notion of stability of approximation for hard optimization tasks and the traveling salesman problem

An Improved Lower Bound on the Approximability of Metric TSP and Approximation Algorithms for the TSP with Sharpened Triangle Inequality