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.

Path-constrained traffic assignment: A trip chain analysis under range anxiety

Abstract: This paper proposes and analyzes a distance-constrained traffic assignment problem with trip chains embedded in equilibrium network flows. The purpose of studying this problem is to develop an appropriate modeling tool for characterizing traffic flow patterns in emerging transportation networks that serve a massive adoption of plug-in electric vehicles. This need arises from the facts that electric vehicles suffer from the “range anxiety” issue caused by the unavailability or insufficiency of public electricity-charging infrastructures and the far-below-expectation battery capacity. It is suggested that if range anxiety makes any impact on travel behaviors, it more likely occurs on the trip chain level rather than the trip level, where a trip chain here is defined as a series of trips between two possible charging opportunities (Tamor et al., 2013). The focus of this paper is thus given to the development of the modeling and solution methods for the proposed traffic assignment problem. In this modeling paradigm, given that trip chains are the basic modeling unit for individual decision making, any traveler’s combined travel route and activity location choices under the distance limit results in a distance-constrained, node-sequenced shortest path problem. A cascading labeling algorithm is developed for this shortest path problem and embedded into a linear approximation framework for equilibrium network solutions. The numerical result derived from an illustrative example clearly shows the mechanism and magnitude of the distance limit and trip chain settings in reshaping network flows from the simple case characterized merely by user equilibrium.

Computing Near-Optimal Solutions to Combinatorial Optimization Problems

Abstract: In the past few years there has been signi cant progress in our understanding of the extent t o w h i c h near optimal solutions can be e ciently computed for NP hard combinatorial optimization problems This paper surveys these recent d e v elopments while concentrating on the ad vances made in the design and analysis of approximation algorithms and in particular on those results that rely on linear programming and its gen eralizations In the past few years there have been major advances in our understanding of performance guarantees for approximation algorithms for NP hard combina torial optimization problems Most notably a f t e r t wenty ve y ears of essentially no progress a new technique has been developed for proving that certain ap proximation algorithms are unlikely to exist Partially in response to this de velopment there have also been signi cant r e c e n t a d v ances in the design and analysis of approximation algorithms In this survey w e will outline a few of the areas in which progress has been made and suggest directions in which there is still interesting work to be done The central de nition of this survey is that of a approximation algorithm for an optimization problem a polynomial time algorithm that delivers a feasible solution of objective function value within a factor of of optimal The study of approximation algorithms predates the theory of NP completeness Some early results such as the proof due to Vizing that a graph always has Mathematics Subject Classi cation Primary C Q C Secondary Q Research partially supported by N S F g r a n t CCR NSF PYI grant CCR with matching support from UPS Sun Proctor Gamble and DuPont and by the Na tional Science Foundation the Air Force O ce of Scienti c Research and the O ce of Naval Research through NSF grant DMS @c American Mathematical Society per page

SRA: Secure Reverse Auction for Task Assignment in Spatial Crowdsourcing

Abstract: In this paper, we study a new type of spatial crowdsourcing, namely competitive detour tasking, where workers can make detours from their original travel paths to perform multiple tasks, and each worker is allowed to compete for preferred tasks by strategically claiming his/her detour costs. The objective is to make suitable task assignment by maximizing the social welfare of crowdsourcing systems and protecting workers’ private sensitive information. We first model the task assignment problem as a reverse auction process. We formalize the winning bid selection of reverse auction as an $n$ n -to-one weighted bipartite graph matching problem with multiple 0-1 knapsack constraints. Since this problem is NP-hard, we design an approximation algorithm to select winning bids and determine corresponding payments. Based on this, a Secure Reverse Auction (SRA) protocol is proposed for this novel spatial crowdsourcing. We analyze the approximation performance of the proposed protocol and prove that it has some desired properties, including truthfulness, individual rationality, computational efficiency, and security. To the best of our knowledge, this is the first theoretically provable secure auction protocol for spatial crowdsourcing systems. In addition, we also conduct extensive simulations on a real trace to verify the performance of the proposed protocol.