Motivated by evidence that parliament seatings are relevant for decision making, we consider the problem to assign seats in a members of parliament. We prove resulting seating assignment is strongly NP-hard several restricted settings. present Mixed Integer Programming formulation problem, describe two families valid inequalities and discuss symmetry-breaking constraints. Further, design heuris...

Among the multitude of activities of Hajj Organization which require careful planning bus assignment to the Iranian pilgrim caravans d g pilgrimage is the most important one. The objective of this assignment is to have a minimum number o standing passengers/empty seats, while satisfying a large number of operational and religious constrain. This problem was formulated as a large scale zero-one ...

A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the to...

The locomotive assignment and the freight train scheduling are important problems in railway transportation. Freight cars are coupled to form a freight rake. The freight rake becomes a train when a locomotive is coupled to it. The locomotive assignment problem assigns locomotives to a set of freight rakes in a way that, with minimum locomotive deadheading time, rake coupling delay and locomotiv...

Training neural networks with discrete stochastic variables presents a unique challenge. Backpropagation is not directly applicable, nor are the reparameterization tricks used in continuous variables. To address this challenge, we present Hindsight Network Credit Assignment (HNCA), novel gradient estimation algorithm for of units. HNCA works by assigning credit to each unit based on degree whic...

stress refers to the degree of force used in producing a syllable. all of the words in lexicon regardless of the apparent structure and the number of their syllables have their own stress. given that the regularities governing stress assignment in persian depend on the type of lexical category and that persian speakers have a tendency to assign stress at the end of words, the goal of the presen...

for a given graph $g=(v,e)$, let $mathscr l(g)={l(v) : vin v}$ be a prescribed list assignment. $g$ is $mathscr l$-$l(2,1)$-colorable if there exists a vertex labeling $f$ of $g$ such that $f(v)in l(v)$ for all $v in v$; $|f(u)-f(v)|geq 2$ if $d_g(u,v) = 1$; and $|f(u)-f(v)|geq 1$ if $d_g(u,v)=2$. if $g$ is $mathscr l$-$l(2,1)$-colorable for every list assignment $mathscr l$ with $|l(v)|geq k$ ...

the prevalent communications networks suffer from lack of spectrum and spectrum inefficiency. this has motivated researchers to develop cognitive radio (cr) as a smart and dynamic radio access promised solution. a major challenge to this new technology is how to make fair assignment of available spectrum to unlicensed users, particularly for smart grids communication. this paper introduces an i...