Efficient Multi-Robot Coverage of a Known Environment

This paper addresses the complete area coverage problem of a known environment by multiple-robots. Complete area coverage is the problem of moving an end-effector over all available space while avoiding existing obstacles. In such tasks, using multiple robots can increase the efficiency of the area coverage in terms of minimizing the operational time and increase the robustness in the face of robot attrition. Unfortunately, the problem of finding an optimal solution for such an area coverage problem with multiple robots is known to be NP-complete. In this paper we present two approximation heuristics for solving the multi-robot coverage problem. The first solution presented is a direct extension of an efficient single robot area coverage algorithm, based on an exact cellular decomposition. The second algorithm is a greedy approach that divides the area into equal regions and applies an efficient single-robot coverage algorithm to each region. We present experimental results for two algorithms. Results indicate that our approaches provide good coverage distribution between robots and minimize the workload per robot, meanwhile ensuring complete coverage of the area.Comment: In proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 201

Parameterized Directed kk-Chinese Postman Problem and kk Arc-Disjoint Cycles Problem on Euler Digraphs

In the Directed $k$-Chinese Postman Problem ($k$-DCPP), we are given a connected weighted digraph $G$ and asked to find $k$ non-empty closed directed walks covering all arcs of $G$ such that the total weight of the walks is minimum. Gutin, Muciaccia and Yeo (Theor. Comput. Sci. 513 (2013) 124--128) asked for the parameterized complexity of $k$-DCPP when $k$ is the parameter. We prove that the $k$-DCPP is fixed-parameter tractable. We also consider a related problem of finding $k$ arc-disjoint directed cycles in an Euler digraph, parameterized by $k$. Slivkins (ESA 2003) showed that this problem is W[1]-hard for general digraphs. Generalizing another result by Slivkins, we prove that the problem is fixed-parameter tractable for Euler digraphs. The corresponding problem on vertex-disjoint cycles in Euler digraphs remains W[1]-hard even for Euler digraphs

Bipartite Graph Packing Problems

The overarching problem of this project was trying to find the maximal number of disjoint subgraphs of a certain type we can pack into any graph. These disjoint graphs could be of any type in the original problem. However, they were limited to be T2 trees for my research (T2 trees are defined in section 2.1 of the paper). In addition, most of my work was focused on packing these T2 trees into constrained bipartite graphs (also defined in section 2.1 of the paper). Even with these specific constraints applied to the overall problem, the project still branched into different subproblems such as packing trees into complete bipartite graphs and finding minimal and maximal bounds for packing these graphs

An overview of vehicular scheduling problems

Work performed under Contract N00014-67-A-0204-0076, Office of Naval Research, Multilevel Logistics Organization Models, NR 347-027, MIT/OSP 81138.Bibliography: leaves 19-21.by Henry Gabbay

Scheduling of Solid Waste Collection Routes

Routing of solid waste collection vehicles in Nigeria poses a challenging task because of attitudinal and haphazard infrastructure problems to contend with. The objective is to minimize the overall cost, which was essentially based on the distance travelled by collection vehicles. The study proposes heuristic methods to generate feasible solution to an extended capacitated Chinese Postman Problem (CCPP) in undirected network. The heuristic procedure consist of “route first, cluster second” and “cluster first, route second” and was applied to scheduling solid waste collection problems in two cities – Abuja and Onitsha. The two techniques were compared and with the existing schedule with respect to cost, efficiency, and distance travelled. A cost model was developed to compare the quality of solution derived. The adoption of the proposed heuristics in Onitsha resulted in reduction of the number of existing vehicles by three, $325.90 (or 7.65$31.10 (or 21.09%) of collection cost per day. Efficiency in refuse collection was increased from 86% to 98% in Abuja and 75% to 95% in Onitsha. The results revealed a good performance of the proposed heuristic methods which will find useful applications in other areas of vehicle scheduling

Solutions to the Chinese Postman Problem

Considering the Chinese Postman Problem, in which a mailman must deliver mail to houses in a neighborhood. The mailman must cover each side of the street that has houses, at least once. The focus of this paper is our attempt to discover the optimal path, or the least number of times each street is walked. The integration of algorithms from graph theory and operations research form the method used to explain solutions to the Chinese Postman Problem

On Diagnosis of Forwarding Plane via Static Forwarding Rules in Software Defined Networks

Software Defined Networks (SDN) decouple the forwarding and control planes from each other. The control plane is assumed to have a global knowledge of the underlying physical and/or logical network topology so that it can monitor, abstract and control the forwarding plane. In our paper, we present solutions that install an optimal or near-optimal (i.e., within 14% of the optimal) number of static forwarding rules on switches/routers so that any controller can verify the topology connectivity and detect/locate link failures at data plane speeds without relying on state updates from other controllers. Our upper bounds on performance indicate that sub-second link failure localization is possible even at data-center scale networks. For networks with hundreds or few thousand links, tens of milliseconds of latency is achievable.Comment: Submitted to Infocom'14, 9 page