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...

this paper proposes a method for ranking decision making units (dmus) using some of the multiple criteria decision making / multiple attribute decision making          (mcdm /madm) techniques, namely, interval analytic hierarchy process (iahp)          and the technique for order preference by similarity to an ideal solution (topsis).          since the efficiency score of unity is assigned to ...

in this paper, we propose an iterated greedy algorithm for solving the blocking flow shop scheduling problem with total flow time minimization objective. the steps of this algorithm are designed very efficient. for generating an initial solution, we develop an efficient constructive heuristic by modifying the best known neh algorithm. effectiveness of the proposed iterated greedy algorithm is t...

a new two-step implicit linear obrechkoff twelfth algebraic order method with vanished phase-lag and its first, second, third and fourth derivatives is constructed in this paper. the purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial schrodinger equation and related problems. this algorithm belongs in the category of the multist...

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 (...

This paper discusses cake-cutting protocols when the cake is a heterogeneous good, represented by an interval on the real line. We propose a new desirable property, the meta-envy-freeness of cake-cutting, which has not been formally considered before. Meta-envy-free means there is no envy on role assignments, that is, no party wants to exchange his/her role in the protocol with the one of any o...

This paper discusses cake-cutting protocols when the cake is a heterogeneous good that is represented by an interval in the real line. We propose a new desirable property, the meta-envy-freeness of cake-cutting, which has not been formally considered before. Though envy-freeness was considered to be one of the most important desirable properties, envy-freeness does not prevent envy about role a...

The current generation of CASE tools mainly provides rigid and unnexible support for editing, storage, veriication and transformation of speciications. Information engineers have to adapt their way of working to CASE tools instead of vice versa. To enable a more exi-ble, method independent, support of information engineers, the concept of a CASE shell has emerged. Crucial for CASE shells is the...

We study classic cake-cutting problems, but in discrete models rather than using infiniteprecision real values, specifically, focusing on their communication complexity. Using general discrete simulations of classical infinite-precision protocols (Robertson-Webb and movingknife), we roughly partition the various fair-allocation problems into 3 classes: “easy” (constant number of rounds of logar...