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.

Online interval scheduling

Abstract: We introduce the online interval scheduling problem, in which a set of intervals of the positive real line is presented to a scheduling algorithm in order of start time. Upon seeing each interval, the algorithm must decide whether or not to “schedule” it. Overlapping intervals may not be scheduled together. We give a strongly 2-competitive algorithm for the case in which intervals must be one of two lengths, either length 1 or length k >> 1. For the general case in which intervals may have arbitrary lengths, A, the ratio of longest to shortest interval, is the important parameter. We give an algorithm with competitive factor O((log A)l+E), and show that no O(logA)-competitive algorithm can exist. Our algorithm need not know the ratio A in advance.

Some New Branching and Bounding Criteria for the Asymmetric Travelling Salesman Problem

Abstract: Many algorithms have been developed for the optimal solution of the asymmetric travelling salesman problem: the most efficient ones are based on the subtour elimination approach. This paper presents a breadth-first branch and bound algorithm which differs from the method of Smith, Srinivasan and Thompson in the selection of the subtour to be split, in the ordering of the arcs in the selected subtour, in the computation of different partial lower bounds and in different data structures to facilitate the updating of the cost matrix. Extensive computational results considering random problems with up to 240 vertices are presented for various ranges of the coefficients of the cost matrix.

Randomized primal-dual analysis of RANKING for online bipartite matching

Abstract: We give a simple proof that the ranking algorithm of Karp, Vazirani and Vazirani [KVV90] is 1-1/e competitive for the online bipartite matching problem. The proof is via a randomized primal-dual argument. Primal-dual algorithms have been successfully used for many online algorithm problems, but the dual constraints are always satisfied deterministically. This is the first instance of a non-trivial randomized primal-dual algorithm in which the dual constraints only hold in expectation. The approach also generalizes easily to the vertex-weighted version considered by Agarwal et al. [AGKM11]. Further we show that the proof is very similar to the deterministic primal-dual argument for the online budgeted allocation problem with small bids (also called the AdWords problem) of Mehta et al. [MSVV05].

On the power assignment problem in radio networks

Abstract: Given a finite set S of points (i.e. the stations of a radio network) on a d-dimensional Euclidean space and a positive integer 1 ≤ h ≤ |S| - 1, the MIN d D h-RANGE ASSIGNMENT problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption, provided that the transmission ranges of the stations ensure the communication between any pair of stations in at most h hops.Two main issues related to this problem are considered in this paper: the trade-off between the power consumption and the number of hops; the computational complexity of the MIN dD h-RANGE ASSIGNMENT problem.As for the first question, we provide a lower bound on the minimum power consumption of stations on the plane for constant h. The lower bound is a function of |S|, h and the minimum distance over all the pairs of stations in S. Then, we derive a constructive upper bound as a function of |S|, h and the maximum distance over all pairs of stations in S (i.e. the diameter of S). It turns out that when the minimum distance between any two stations is "not too small" (i.e. well spread instances) the upper bound matches the lower bound. Previous results for this problem were known only for very special 1-dimensional configurations (i.e., when points are arranged on a line at unitary distance) [Kirousis, Kranakis, Krizanc and Pelc, 1997].As for the second question, we observe that the tightness of our upper bound implies that MIN 2D h-RANGE ASSIGNMENT restricted to well spread instances admits a polynomial time approximation algorithm. Then, we also show that the same approximation result can be obtained for random instances. On the other hand, we prove that for h=|S|-1 (i.e. the unbounded case) MIN 2D h-RANGE ASSIGNMENT is NP-hard and MIN 3D h-RANGE ASSIGNMENT is APX-complete.

Mathematical Techniques for Efficient Record Segmentation in Large Shared Databases

Abstract: It is possible to significantly reduce the average cost of information retrieval from a large shared database by partitioning data items stored within each record into a primary and a secondary record segment. An analytic model, based upon knowledge of data item lengths, transportation costs, and retrieval patterns, is developed to assist an analyst with this assignment problem. The model is generally applicable to environments in which a database resides in secondary storage, and is useful for both uniprogramming and multiprogramming systems. A computationally tractable record design algorithm has been implemented as a Fortran program and applied to numerous problems. Realistic examples are presented which demonstrate a potential for reducing total system cost by more than 65 percent.