In which we show how to find the eigenvalues and eigenvectors of Cayley graphs of Abelian groups, we find tight examples for various results that we proved in earlier lectures, and, along the way, we develop the general theory of harmonic analysis which includes the Fourier transform of periodic functions of a real variable, the discrete Fourier transform of periodic functions of an integer var...

AND/OR search spaces have recently been introduced as a unifying paradigm for advanced algorithmic schemes for graphical models. The main virtue of this representation is its sensitivity to the structure of the model, which can translate into exponential time savings for search algorithms. In this paper we extend the recently introduced AND/OR Branch-and-Bound algorithm (AOBB) [1] for solving p...

A key feature of constraint programming is the ability to design specific search strategies to solve problems. On the contrary, integer programming solvers have used efficient general-purpose strategies since their earliest implementations. We present a new general purpose search strategy for constraint programming inspired from integer programming techniques and based on the concept of the imp...

A major challenge in the initial stage of production planning for the steel industry is the material allocation problem (MAP): finding the best match of orders and materials (steel slabs and coils) with respect to an objective function that takes into account order due dates, preferences for matches, allocated weights, surplus weights of materials, and other factors. The MAP is NP-hard and is d...

This paper reports the effect of functional roles on computer-supported collaborative learning. Thirtythree students in ten groups, equally distributed over two research conditions (role versus nonrole), returned an evaluation questionnaire assessing their computer-supported collaborative learning experience. Principal axis factoring revealed a latent variable interpreted as: perceived group ef...

The satisfiability and finite satisfiability problems for the two-variable fragment of first-order logic with counting were shown in [5] to be in NExpTime. This paper presents a simplified proof via a result on integer programming due to Eisenbrand and Shmonina [2].

Labor is a crucial resource in most organizations. In not-for-profit, public, and government services, it is common for labor to include unpaid volunteers. This article demonstrates how the volunteer labor assignment (VLA) problem is markedly different from traditional labor assignment (TLA) problems such as labor scheduling. One core difference pertains to the cost structure of labor, where TL...

A Video-on-Demand system usually consists of a large number of independent video servers. In order to utilize network resources as efficiently as possible the overall network load should be balanced among the available servers. We consider a problem formulation based on an estimation of the expected number of requests per movie during the period of highest user interest. Apart from load balanci...

We propose two mixed-integer linear programming based approaches for the 2-D orthogonal strip packing problem. Using knowledge from the alternative forms of time representation in scheduling formulations, we show how to efficiently combine three different concepts into the xand ydimensions. One model features a discrete representation on the x-axis (strip width) and a continuous representation ...

We consider the allocation of a limited budget to a set of activities or investments in order to maximize return from investment. In a number of practical contexts (e.g., advertising), the return from investment in an activity is effectively modeled using an S-curve, where increasing returns to scale exist at small investment levels, and decreasing returns to scale occur at high investment leve...