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Full-Text Articles in Discrete Mathematics and Combinatorics
Of Matroid Polytopes, Chow Rings And Character Polynomials, Ahmed Ashraf
Of Matroid Polytopes, Chow Rings And Character Polynomials, Ahmed Ashraf
Electronic Thesis and Dissertation Repository
Matroids are combinatorial structures that capture various notions of independence. Recently there has been great interest in studying various matroid invariants. In this thesis, we study two such invariants: Volume of matroid base polytopes and the Tutte polynomial. We gave an approach to computing volume of matroid base polytopes using cyclic flats and apply it to the case of sparse paving matroids. For the Tutte polynomial, we recover (some of) its coefficients as degrees of certain forms in the Chow ring of underlying matroid. Lastly, we study the stability of characters of the symmetric group via character polynomials. We show …
Approximation Algorithms For Problems In Makespan Minimization On Unrelated Parallel Machines, Daniel R. Page
Approximation Algorithms For Problems In Makespan Minimization On Unrelated Parallel Machines, Daniel R. Page
Electronic Thesis and Dissertation Repository
A fundamental problem in scheduling is makespan minimization on unrelated parallel machines (R||Cmax). Let there be a set J of jobs and a set M of parallel machines, where every job Jj ∈ J has processing time or length pi,j ∈ ℚ+ on machine Mi ∈ M. The goal in R||Cmax is to schedule the jobs non-preemptively on the machines so as to minimize the length of the schedule, the makespan. A ρ-approximation algorithm produces in polynomial time a feasible solution such that its objective value is within a multiplicative factor ρ of …