Scalable Algorithms for Server Allocation in Infostations

Author(s):  
Alan A. Bertossi ◽  
M. Cristina Pinotti ◽  
Phalguni Gupta

The server allocation problem arises in isolated infostations, where mobile users going through the coverage area require immediate high-bit rate communications such as web surfing, file transferring, voice messaging, email and fax. Given a set of service requests, each characterized by a temporal interval and a category, an integer k, and an integer hc for each category c, the problem consists in assigning a server to each request in such a way that at most k mutually simultaneous requests are assigned to the same server at the same time, out of which at most hc are of category c, and the minimum number of servers is used. Since this problem is computationally intractable, a scalable 2-approximation online algorithm is exhibited. Generalizations of the problem are considered, which contain bin-packing, multiprocessor scheduling, and interval graph coloring as special cases, and admit scalable on-line algorithms providing constant approximations.

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 735
Author(s):  
Tomasz Dzido ◽  
Renata Zakrzewska

We consider the important generalisation of Ramsey numbers, namely on-line Ramsey numbers. It is easiest to understand them by considering a game between two players, a Builder and Painter, on an infinite set of vertices. In each round, the Builder joins two non-adjacent vertices with an edge, and the Painter colors the edge red or blue. An on-line Ramsey number r˜(G,H) is the minimum number of rounds it takes the Builder to force the Painter to create a red copy of graph G or a blue copy of graph H, assuming that both the Builder and Painter play perfectly. The Painter’s goal is to resist to do so for as long as possible. In this paper, we consider the case where G is a path P4 and H is a path P10 or P11.


1990 ◽  
Vol 4 (4) ◽  
pp. 447-460 ◽  
Author(s):  
Coastas Courcobetis ◽  
Richard Weber

Items of various types arrive at a bin-packing facility according to random processes and are to be combined with other readily available items of different types and packed into bins using one of a number of possible packings. One might think of a manufacturing context in which randomly arriving subassemblies are to be combined with subassemblies from an existing inventory to assemble a variety of finished products. Packing must be done on-line; that is, as each item arrives, it must be allocated to a bin whose configuration of packing is fixed. Moreover, it is required that the packing be managed in such a way that the readily available items are consumed at predescribed rates, corresponding perhaps to optimal rates for manufacturing these items. At any moment, some number of bins will be partially full. In practice, it is important that the packing be managed so that the expected number of partially full bins remains uniformly bounded in time. We present a necessary and sufficient condition for this goal to be realized and describe an algorithm to achieve it.


Author(s):  
Q. J. Ge ◽  
B. Ravani

Abstract This paper follows a previous one on the computation of spatial displacements (Ravani and Ge, 1992). The first paper dealt with the problem of computing spatial displacements from a minimum number of simple features of points, lines, planes, and their combinations. The present paper deals with the same problem using a redundant set of the simple geometric features. The problem for redundant information is formulated as a least squares problem which includes all simple features. A Clifford algebra is used to unify the handling of various feature information. An algorithm for determining the best orientation is developed which involves finding the eigenvector associated with the least eigenvalue of a 4 × 4 symmetric matrix. The best translation is found to be a rational cubic function of the best orientation. Special cases are discussed which yield the best orientation in closed form. In addition, simple algorithms are provided for automatic generation of body-fixed coordinate frames from various feature information. The results have applications in robot and world model calibration for off-line programming and computer vision.


Author(s):  
Morgan Magnin ◽  
Guillaume Moreau ◽  
Nelle Varoquaux ◽  
Benjamin Vialle ◽  
Karen Reid ◽  
...  

A critical component of the learning process lies in the feedback that students receive on their work that validates their progress, identifies flaws in their thinking, and identifies skills that still need to be learned. Many higher-education institutions have developed an active pedagogy that gives students opportunities for different forms of assessment and feedback. This means that students have numerous lab exercises, assignments, and projects. Both instructors and students thus require effective tools to efficiently manage the submission, assessment, and individualized feedback of students’ work. The open-source web application MarkUs aims at meeting these needs: it facilitates the submission and assessment of students’ work. Students directly submit their work using MarkUs, rather than printing it, or sending it by email. The instructors or teaching assistants use MarkUs’s interface to view the students’ work, annotate it, and fill in a marking rubric. Students use the same interface to read the annotations and learn from the assessment. Managing the students’ submissions and the instructors assessments within a single online system, has led to several positive pedagogical outcomes: the number of late submissions has decreased, the assessment time has been drastically reduced, students can access their results and read the instructor’s feedback immediately after the grading process is completed. Using MarkUs has also significantly reduced the time that instructors spend collecting assignments, creating the marking schemes, passing them on to graders, handling special cases, and returning work to the students. In this paper, we introduce MarkUs’ features, and illustrate their benefits for higher education through our own teaching experiences and that of our colleagues. We also describe an important benefit of the fact that the tool itself is open-source. MarkUs has been developed entirely by students giving them a valuable learning opportunity as they work on a large software system that real users depend on. Virtuous circles indeed arise, with former users of MarkUs becoming developers and then supervisors of further development. We will conclude by drawing perspectives about forthcoming features and use, both technically and pedagogically.


10.37236/6516 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Megumi Asada ◽  
Ryan Chen ◽  
Florian Frick ◽  
Frederick Huang ◽  
Maxwell Polevy ◽  
...  

Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in Euclidean $d$-space that guarantees any such point set admits a partition into $r$ parts, any $k$ of whose convex hulls intersect. Here we give new and improved lower bounds for this number, which Reay conjectured to be independent of $k$. We prove a colored version of Reay's conjecture for $k$ sufficiently large, but nevertheless $k$ independent of dimension $d$. Pairwise intersecting convex hulls have severely restricted combinatorics. This is a higher-dimensional analogue of Conway's thrackle conjecture or its linear special case. We thus study convex-geometric and higher-dimensional analogues of the thrackle conjecture alongside Reay's problem and conjecture (and prove in two special cases) that the number of convex sets in the plane is bounded by the total number of vertices they involve whenever there exists a transversal set for their pairwise intersections. We thus isolate a geometric property that leads to bounds as in the thrackle conjecture. We also establish tight bounds for the number of facets of higher-dimensional analogues of linear thrackles and conjecture their continuous generalizations.


2004 ◽  
Vol 143 (1-3) ◽  
pp. 238-251 ◽  
Author(s):  
Luitpold Babel ◽  
Bo Chen ◽  
Hans Kellerer ◽  
Vladimir Kotov

1985 ◽  
Vol 32 (3) ◽  
pp. 562-572 ◽  
Author(s):  
C. C. Lee ◽  
D. T. Lee

Author(s):  
Aida Kenza Amara ◽  
Bachir Djebbar

The two-dimensional bin packing problem involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. In this paper, we propose and develop mathematically a new pretreatment for the oriented version of the problem in order to reduce its size, identify and value the lost spaces by increasing the size of some objects. A heuristic method based on the first-fit strategy adapted to this problem is proposed. We present an approach of resolution using the bee colony optimization. The computational results show the effectiveness of the pretreatment in reducing the number of bins.


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