Assignment problem

About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.

A branch-and-price algorithm for the capacitatedp-median problem

Abstract: The capacitated p-median problem is the variation of the well-known p-median problem in which a demand is associated to each user, a capacity is associated to each candidate median, and the total demand of the users associated to the same median must not exceed its capacity. We present a branch-and-price algorithm, that exploits column generation, heuristics and branchand-bound to compute optimal solutions. We compare our branch-and-price algorithm with other methods proposed so far, and we present computational results both on test instances taken from the literature and on random instances with different values of the ratio between the number of medians and the number of users. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 45(3), 125–142 2005

A distributed algorithm for the multi-robot task allocation problem

Abstract: In this work we address the Multi-Robot Task Allocation Problem (MRTA). We assume that the decision making environment is decentralized with as many decision makers (agents) as the robots in the system. To solve this problem, we developed a distributed version of the Hungarian Method for the assignment problem. The robots autonomously perform different substeps of the Hungarian algorithm on the base of the individual and the information received through the messages from the other robots in the system. It is assumed that each robot agent has an information regarding its distance from the targets in the environment. The inter-robot communication is performed over a connected dynamic communication network and the solution to the assignment problem is reached without any common coordinator or a shared memory of the system. The algorithm comes up with a global optimum solution in O(n3) cumulative time (O(n2) for each robot), with O(n3) number of messages exchanged among the n robots.

A robust approach to the UAV task assignment problem

Abstract: This paper presents a new robust approach to the task assignment of unmanned aerial vehicles (UAVs) operating in uncertain dynamic environments for which the optimization data, such as target cost and target–UAV distances, are time varying and uncertain. The impact of this uncertainty in the data is mitigated by tightly integrating two approaches for improving the robustness of the assignment algorithm. One approach is to design task assignment plans that are robust to the uncertainty in the data, which reduces the sensitivity to errors in the situational awareness (SA), but can be overly conservative for long duration plans. A second approach is to replan as the SA is updated, which results in the best plan given the current information, but can lead to a churning type of instability if the updates are performed too rapidly. The strategy proposed in this paper combines robust planning with the techniques developed to eliminate churning. This combination results in the robust filter-embedded task assignment algorithm that uses both proactive techniques that hedge against the uncertainty, and reactive approaches that limit churning behavior by the vehicles. Numerous simulations are shown to demonstrate the performance benefits of this new algorithm. Copyright © 2007 John Wiley & Sons, Ltd.

Optimality of Treating Interference as Noise: A Combinatorial Perspective

Abstract: For single-antenna Gaussian interference channels, we reformulate the problem of determining the generalized degrees of freedom (GDoF) region achievable by treating interference as Gaussian noise (TIN) derived by Geng et al. from a combinatorial optimization perspective. We show that the TIN power control problem can be cast into an assignment problem, such that the globally optimal power allocation variables can be obtained by well-known polynomial time algorithms (e.g., centralized Hungarian method or distributed Auction algorithm). Furthermore, the expression of the TIN-achievable GDoF region (TINA region) can be substantially simplified with the aid of maximum weighted matchings. We also provide conditions under which the TINA region is a convex polytope that relax those by Geng et al. For these new conditions, together with a channel connectivity (i.e., interference topology) condition, we show TIN optimality for a new class of interference networks that is not included, nor includes, the class found by Geng et al. Building on the above insights, we consider the problem of joint link scheduling and power control in wireless networks, which has been widely studied as a basic physical layer mechanism for device-to-device communications. Inspired by the relaxed TIN channel strength condition as well as the assignment-based power allocation, we propose a low-complexity GDoF-based distributed link scheduling and power control mechanism (ITLinQ+) that improves upon the ITLinQ scheme proposed by Naderializadeh and Avestimehr and further improves over the heuristic approach known as FlashLinQ. It is demonstrated by simulation that ITLinQ+ without power control provides significant average network throughput gains over both ITLinQ and FlashLinQ, and yet still maintains the same level of implementation complexity. Furthermore, when ITLinQ+ is augmented by power control, it provides an energy efficiency substantially larger than that of ITLinQ and FlashLinQ, at the cost of additional complexity and some signaling overhead.