We develop the rst explicit procedures for exact envy-free chore division for 4 or more players. We also give a simple 3-person procedure. Our 4-person moving-knife scheme and n-person discrete algorithm are accomplished by exploiting a notion of \irrevocable advantage" for chores, and are motivated by similar solutions for cake-cutting by Brams, Taylor, and Zwicker. We discuss the diierences b...

It is well-known that the central limit theorem holds for partial sums of a stationary sequence (Xi) of m-dependent random variables with finite variance; however, the limit may be degenerate with variance 0 even if Var(Xi) 6= 0. We show that this happens only in the case when Xi − EXi = Yi − Yi−1 for an (m − 1)-dependent stationary sequence (Yi) with finite variance (a result implicit in earli...

The problem of fairly dividing a cake (as a metaphor for a heterogeneous divisible good) has been the subject of much interest since the 1940’s, and is of importance in multiagent resource allocation. Two fairness criteria are usually considered: proportionality, in the sense that each of the n agents receives at least 1/n of the cake; and the stronger property of envy-freeness, namely that eac...

Requirements engineering is a core practice within eXtreme Programming. Practising teams learn to not abandon any of the interconnected core practices. The continuous feedback teaches the team that they will develop at a faster and more reliable pace with the full set of practices. This paper shares an experience of how teams could accelerate development out of necessity, while maintaining thei...

This paper presents an early empirical study on Extreme Programming practices employing a qualitative action research method. The study was conducted on university students doing real commercial development projects to gain an insight into the problems faced by the new developers in adopting these agile practices. The aim of the study was to investigate the effects of the XP practices on the qu...

This research proposes a new ranking system for extreme efficient DMUs (Decision Making Units) based upon the omission of these efficient DMUs from reference set of the inefficient DMUs. We state and prove some facts related to our model. A numerical example where the proposed method is compared with traditional ranking approaches is shown. 2006 Elsevier B.V. All rights reserved.

There is a heterogeneous resource that contains both good parts and bad parts, for example, a cake with some parts burnt, a land-estate with some parts heavily taxed, or a chore with some parts fun to do. The resource has to be divided fairly among n agents, each of whom has a personal value-density function on the resource. The value-density functions can accept any real value positive or nega...

If Ill' ... , ~tn are non-atomic probability measures on the same measurable space (S, ff"), then there is an ff"-measurable partition {AJ7= 1 of S so that IlJAi)~(n-l+m)-l for all i=I, ... ,n, where m=l l i 01 lli l l is the total mass of the largest measure dominated by each of the Il/s; moreover, this bound is attained for all n ~ 1 and all m in [0,1]. This result is an analog of the bound (...