Michael Forbes

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Vehicle routing problems attempt to define optimal delivery methods of goods to places. I examined the capacitated vehicle routing problem that determines the least cost route to deliver objects to customers using a single vehicle of fixed capacity. Vehicle routing problems attract considerable attention because of their implications for delivery(More)
Research in the last decade has shown that to prove lower bounds or to derandomize polynomial identity testing (PIT) for general arithmetic circuits it suffices to solve these questions for restricted circuits. In this work, we study the smallest possibly restricted class of circuits, in particular depth-4 circuits, which would yield such results for(More)
This is a survey of pseudorandomness, the theory of efficiently generating objects that “look random” despite being constructed using little or no randomness. This theory has significance for a number of areas in computer science and mathematics, including computational complexity, algorithms, cryptography, combinatorics, communications, and additive number(More)
Research in the last decade has shown that to prove lower bounds or to derandomize polynomial identity testing (PIT) it suffices to solve these questions for restricted circuits. In this work, we study the possibly most restricted class of circuits, within depth-4, which would yield such results for general circuits (that is, the complexity class VP). We(More)
We first motivate coding theory as a topic. Consider the problem of storing data on a CD-ROM (or a modern variant). Such physical devices can be corrupted over time due to mistreatment or decay of physical structure. That is, errors will occur in our stored message. Thus, if we want to recover the original message in the future we need to do something to(More)
The Ideal Membership Problem is as follows: given f0, f1, . . . , fm ∈ K[x1, . . . , xn], is f0 ∈ 〈f1, . . . , fm〉, where 〈f1, . . . , fm〉 denotes the ideal generated by the fi? An equivalent formulation is: are there q1, . . . , qm ∈ K[x1, . . . , xn] such that f0 = ∑m i=1 qifi? We will solve this question by using Gröbner bases. That is, a Gröbner basis(More)