Competitive analysis of repeated greedy auction algorithm for online multi-robot task assignment

We present distributed algorithms for multirobot task assignment where the tasks have to be completed within given deadlines. Each robot has a limited battery life and thus there is an upper limit on the amount of time that it has to perform tasks. Performing each task requires certain amount of time (called the task duration) and each robot can have different payoffs for the tasks. Our problem is to assign the tasks to the robots such that the total payoff is maximized while respecting the task deadline constraints and the robot's battery life constraints. Our problem is NP-hard since a special case of our problem is the classical generalized assignment problem (which is NP-hard). There are no known algorithms (distributed or centralized) for this problem with provably good guarantees of performance. We present a distributed algorithm for solving this problem and prove that our algorithm has an approximation ratio of 2. For the special case of constant task duration we present a distributed algorithm that is provably almost optimal. Our distributed algorithms are polynomial in the number of robots and the number of tasks. We also present simulation results to depict the performance of our algorithms. Note to Practitioners-In this paper, we present provably good multirobot task assignment algorithms, while considering practical constraints like task deadlines and limited battery life of robots. Such constraints are relevant in many applications including parts movement by robots in manufacturing, delivery of goods by unmanned vehicles, and search and rescue operations. Our solution is applicable to a group of heterogeneous robots with different suitability (i.e., payoffs) for different tasks. Our distributed approach is independent of the underlying robot communication network topology, and thus can be applied to a wide range of robot network deployments. Finally, our approach is easy to implement, has low communication requirements, and it is scalable, since its running time is linear in the number of robots and tasks.

High-performance computing systems typically employ heterogeneous multicore design to improve both execution performance and efficiency. Task assignment is critical in exploiting the diversity of computation capability, energy consumption, as well as communication cost on heterogeneous multicore processors. In this paper, we explore the opportunity of task assignment on heterogeneous multicore processors to minimize execution and communication costs considering time constraint. The general heterogeneous task assignment problem is NP-Complete. However, we find that optimal task assignment can be achieved for widely used, tree-shaped task graphs using dynamic programming. We first propose a dynamic programming algorithm, the Optimal Tree Assign (OTA) algorithm, to generate optimal assignments for trees. Then, we develop the Integer Linear Programming model of the general task assignment problem for Directed Acyclic Graphs. A polynomial-time heuristic, the Extended Tree Assignment algorithm, is also proposed to produce near-optimal solutions for the general heterogeneous task assignment problem efficiently. The experimental results show that the proposed algorithms outperform both homogeneous task assignment method and greedy strategy for all the benchmarks. The OTA algorithm reduces the total system time by 42.5 percent and 23.5 percent on average compared with the homogeneous task assignment method and greedy algorithm, respectively.

This paper proposed an unmanned air vehicle (UAV) swarm task and resource dynamic assignment algorithm based on task sequence mechanism. By establishing a task sequence, each UAV strictly separates the necessary task time and synchronization waiting time. For the found new targets, each UAV quickly determines its available time period. According to the available time and task resources, an auction algorithm and consensus algorithm are used to decompose the task assignment into initial distributed assignment phase and swarm consensus phase to develop real-time conflict-free task solutions for UAV swarm. The simulation experiment verified that the algorithm could assign different tasks to UAVs in a real-time distributed manner with the limited resources of each UAV.

This works develops a novel hierarchical algorithm for task assignment (TA), coordination and communication of multiple UAVs engaging multiple targets and conceives an ad-hoc routing algorithm for synchronization of target lists utilizing a distributed computing topology. Assuming limited communication bandwidth and range, coordination of UAV motion is achieved by implementing a simple behavioral flocking algorithm utilizing a tree topology for target list routing. The TA algorithm is based on a graph-theoretic approach, in which a node locates all the detectable targets, identifies them and computes its distance to each target. The node then produces an attack plan that minimizes the sum of distances of the UAVs in the subtree of a given node to the targets. Simulation experiments show that the combination of flocking and TA algorithms gives the best performance. Clear-cut advantages of the TA algorithm are shown to exist in cases where the hit probability tends to one. An improvement of efficiency, representing the ratio between killed targets and the number of missile launches, is obtained for larger numbers of UAVs only if the engagement times are long enough, utilizing the improved coverage achieved by more UAVs.

This paper investigates the duration-aware task assignment problem for heterogeneous mobility users in MCS (DTAH problem). There are two types of users in MCS, vehicle users and pedestrian users. The vehicle user gets to the task fast, but the task duration is short. Pedestrian user meets the task duration limit, but it takes a long time to reach the task. Given a set of tasks and two types of users, each user, and each task has a duration limit. The DTAH problem is how to assign tasks to maximize the utility of the system. We prove that the DTAH problem is NP-hard by reducing the weighted maximum set coverage problem to the DTAH problem. Then, we solve the problem from a pedestrian perspective and a vehicle perspective. From the pedestrian user perspective, we propose a pedestrian user task assignment (PTA) algorithm based on the Kuhn-Munkres algorithm. From the vehicle user perspective, we propose a greedy vehicle user task assignment (VTA) algorithm. We prove that the VTA algorithm can obtain the approximate ratio of 1-1/e to the optimal value. Finally, we design the heterogeneous user task assignment (HTA) algorithm based on these PTA and VTA algorithms. Extensive experiments have proved that our proposed HTA algorithm achieves more efficient performance than other comparison algorithms.

For the large-scale operations of unmanned aerial vehicle (UAV) swarm and the large number of UAVs, this paper proposes a two-layer task and resource assignment algorithm based on feature weight clustering. According to the numbers and types of task resources of each UAV and the distances between different UAVs, the UAV swarm is divided into multiple UAV clusters, and the large-scale allocation problem is transformed into several related small-scale problems. A two-layer task assignment algorithm based on the consensus-based bundle algorithm (CBBA) is proposed, and this algorithm uses different consensus rules between clusters and within clusters, which ensures that the UAV swarm gets a conflict-free task assignment solution in real time. The simulation results show that the algorithm can assign tasks effectively and efficiently when the number of UAVs and targets is large.

Data association is a critical problem in multitarget tracking. In fact, it is the bottleneck of most of the multitarget tracking algorithms such as multiple hypothesis tracker (MHT). In this paper, we propose a heuristic assignment algorithm which determine approximately the N best data association hypotheses in an efficient manner. This greedy algorithm is based on the branch and bound concept and has the flexibility of adapting to various scenarios. Performance evaluation of the algorithm based on simulation is also presented.

Wireless sensor networks have recently posed many new system building challenges. One of the main problems is energy conservation since most of the sensors are devices with limited battery life and it is infeasible to replenish energy via replacing batteries. An effective approach for energy conservation is scheduling sleep intervals for some sensors, while the remaining sensors stay active providing continuous service. In this paper we consider the problem of selecting a set of active sensors of minimum cardinality so that sensing coverage and network connectivity are maintained. We show that the greedy algorithm that provides complete coverage has an approximation factor of Ω(log n), where n is the number of sensor nodes. Then we present algorithms that provide approximate coverage while the number of nodes selected is a constant factor far from the optimal solution.

A Connected Dominating Set (CDS) of a graph representing a Wireless Sensor Network can be used as a virtual backbone for routing through the network. Since the sensors in the network are constrained by limited battery life, we desire a minimal CDS for the network, a known NP-hard problem. In this paper we present three randomized algorithms for constructing a CDS. We evaluate our algorithms using simulations and compare them to the two-hop K2 algorithm and two other greedy algorithms from the literature. After pruning, the randomized algorithms construct a CDS that are generally equivalent in size to those constructed by K2 while being asymptotically better in time and message complexity. This shows the potential of significant energy savings in using a randomized approach as a result of the reduced complexity.

With the advent of intelligent technology, the users of spatio-temporal crowdsourcing and their participation in the crowdsourcing tasks continue to increase exponentially. This poses new challenges to the crowdsourcing field. One of the core research areas of spatio-temporal crowdsourcing is task assignment. Most of the existing research on task assignment is focused on offline optimal task assignment, where, the platform has already learned all the information about workers and tasks beforehand. However, these studies cannot obtain good results in real-world situations. At the same time, online task assignment problems often result in local optimal assignment. To solve these problems, more attention needs to be paid to online task assignments and the arrival time of workers. This paper proposes an Online Bilateral Assignment (OBA) problem based on the online assignment model. The competitive ratio of the Greedy algorithm is analyzed according to the OBA problem model. Also, another solution to the OBA problem according to the Greedy algorithm, the Improved-Baseline algorithm, is proposed. Additionally, a Bilateral Online Priority Reassignment algorithm (BOPR) is proposed. The BOPR algorithm realizes real-time task/worker assignment through the bilateral assignment as a solution for online task assignment. In order to guarantee the number of matching tasks, a priority queue is designed in the BOPR algorithm. Considering the waiting time deadlines of tasks and workers and the error rate for priority ranking, it avoids tasks and workers waiting too long and assigns each task to the best possible extent. On this basis, a two-stage assignment strategy is designed for unsuccessful tasks, which could minimize the error rate of the task and significantly improve the efficiency of task assignment. Finally, through experiments on real data sets, the algorithm's performance in terms of global utility value and the number of matches is evaluated.

A channel scheduling problem for a given graph G(V,E) is to select a subset E′ of edges of E and assign channel to each one in E′ under the restriction that all edges of E′ are interference free. We introduce the notion of two sides approximation for the channel scheduling problem. A pair of parameters (f,g) controls the accuracy of approximation in this paper. A (f,g)-approximation satisfies \(\sum_{e\in E'}W(e)\ge{\sum_{e\in Opt}W(e)\over f}\) and \(\sum_{e\in E-E'}W(e)\le g\sum_{e\in E- Opt^*}W(e)\), where Opt * is the set of edges assigned channels in an optimal solution, and W(e) is the weight of edge e. An f-approximation satisfies \(\sum_{e\in E'}W(e)\ge{\sum_{e\in Opt}W(e)\over f}\). We show that a simple greedy algorithm can obtain an (O(1), O(1))-approximation for the single channel scheduling problem. In many cases, the greedy algorithms gives much more accurate result than the worst ratio. Furthermore, we develop an \(|E|^{O({1\over \epsilon})}\) time (1 − ε, O(1))-approximation algorithm for the single channel scheduling problem. We also show that a simple greedy algorithm can obtain an O(1)-approximation for the multi-channel scheduling problem which satisfies \(\sum_{e\in E'}W(e)\ge{\sum_{e\in Opt}W(e)\over \Omega(1)}\). We also develop a \(|E|^{O({d\over \epsilon})}\) time (1 − ε)-approximation algorithm the multi-channel scheduling problem, where d is the number of channels. This improves the existing approximation scheme for multi-channel scheduling problem with \(|E|^{O({d\over \epsilon^2})}\) time by Cheng et al. We also develop a polynomial time constant factor greedy approximation algorithm for the multi-channel scheduling that allows variate radii of interference among those nodes.

This paper addresses task assignment problem fortree-structure task model on heterogeneous multicore embedded systems with time constraint considering both execution time and communication load. The goal is to minimize the total system cost for a given task graph representing a set of tasks and data dependencies in a heterogeneous multicore systemwhile the time constraint is satisfied. Instead of assigning all the tasks to processors of the same type in a homogeneous environment, heterogeneous task assignment usually can reduce the system cost by exploring various capacities and costs in a heterogeneous multicore system. The general heterogeneous assignment problem is NP-complete. In this paper, we show that optimal task assignment can be found for some widely-used, special task graphs, such as tree-structure graph, using dynamic programming. A dynamic programming algorithm, the Tree Assign (TA) algorithm, is proposed in this paper to solve the heterogeneous task assignment problem for tree-structure task graphs. The experimental results show that our algorithm reduces the total system cost by 31.8% compared with assignment results on homogeneous multicore systems. Also, our algorithm achieves an average cost reduction by 21.9% compared with greedy algorithm.

This work develops distributed hierarchical task assignments and communication algorithms for flocks of unmanned aerial vehicles dispersed in an unknown theater while engaging multiple moving targets. The dynamical changes require distributed algorithms, without relying on a central agent, which may constitute a single point-of-failure and is exposed to communication breaks. Our methodology overcomes the typical deficiencies of a centralized solution by organizing the agents in spanning trees. Whenever possible, the spanning trees merge into a single tree that clusters the maximum number of agents. Using relaxation methods and inputs from its parent and children, every agent attempts to optimize its own solution for task assignment while communicating using an ad-hoc protocol. Simulation experiments show clear-cut advantages of using the proposed task assignment and communication algorithms.

The existing task assignment algorithms usually solve only a point-based model. This paper proposes a novel algorithm for task assignment in detection search tasks. Firstly, the optimal reconnaissance path is generated by considering the drone’s position and attitude information, as well as the type of heterogeneous targets present in the actual scene. Subsequently, an adaptive crowding distance calculation (ACD-NSGA-II) is proposed based on the relative position of solutions in space, taking into account the spatial distribution of parent solutions and constraints imposed by uncertain targets and terrain. Finally, comparative experiments using digital simulation are conducted under two different target probability scenarios. Moreover, the improved algorithm is further evaluated across 100 cases, and a comparison of the Pareto solution set with other algorithms is conducted to demonstrate the algorithm’s overall adaptability.

In this paper, we consider the on-line single machine scheduling of unit time jobs with rejection. All jobs arrive on-line over a list (one by one). For each arriving job, the on-line algorithm must decide immediately to accept or reject it. The objective is to minimize the maximum quadratic completion time of accepted jobs plus the total rejection cost of rejected jobs. For this problem, we show that 1.7299 is a lower bound on the competitive ratio and present a simple greedy algorithm with the competitive ratio 2. Furthermore, we also provide a modified greedy algorithm with a better competitive ratio [Formula: see text].