Polynomial Time Instances for the IKHO Problem

The Interactive Knapsacks Heuristic Optimization (IKHO) problem is a particular knapsacks model in which, given an array of knapsacks, every insertion in a knapsack affects also the other knapsacks, in terms of weight and profit. The IKHO model was introduced by Isto Aho to model instances of the load clipping problem. The IKHO problem is known to be APX-hard and, motivated by this negative fact, Aho exhibited a few classes of polynomial instances for the IKHO problem. These instances were obtained by limiting the ranges of two structural parameters, c and u, which describe the extent to which an insertion in a knapsack influences the nearby knapsacks. We identify a new and broad class of instances allowing for a polynomial time algorithm. More precisely, we show that the restriction of IKHO to instances where (c + 2u)/c is bounded by a constant can be solved in polynomial time, using dynamic programming

An Implementation of the Chor-Rivest Knapsack Type Public Key Cryptosystem

The Chor-Rivest cryptosystem is a public key cryptosystem first proposed by MIT cryptographers Ben Zion Chor and Ronald Rivest [Chor84]. More recently Chor has imple mented the cryptosystem as part of his doctoral thesis [Chor85]. Derived from the knapsack problem, this cryptosystem differs from earlier knapsack public key systems in that computa tions to create the knapsack are done over finite algebraic fields. An interesting result of Bose and Chowla supplies a method of constructing higher densities than previously attain able [Bose62]. Not only does an increased information rate arise, but the new system so far is immune to the low density attacks levied against its predecessors, notably those of Lagarias- Odlyzko and Radziszowski-Kreher [Laga85, Radz86]. An implementation of this cryptosystem is really an instance of the general scheme, dis tinguished by fixing a pair of parameters, p and h , at the outset. These parameters then remain constant throughout the life of the implementation (which supports a community of users). Chor has implemented one such instance of his cryptosystem, where p =197 and h =24. This thesis aspires to extend Chor\u27s work by admitting p and h as variable inputs at run time. In so doing, a cryptanalyst is afforded the means to mimic the action of arbitrary implementations. A high degree of success has been achieved with respect to this goal. There are only a few restrictions on the choice of parameters that may be selected. Unfortunately this general ity incurs a high cost in efficiency; up to thirty hours of (VAX1 1-780) processor time are needed to generate a single key pair in the desired range (p = 243 and h =18)

Notes for Miscellaneous Lectures

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.Comment: 6 pages. New section 6 adde

Incorporating Behavioral Constraints in Online AI Systems

AI systems that learn through reward feedback about the actions they take are increasingly deployed in domains that have significant impact on our daily life. However, in many cases the online rewards should not be the only guiding criteria, as there are additional constraints and/or priorities imposed by regulations, values, preferences, or ethical principles. We detail a novel online agent that learns a set of behavioral constraints by observation and uses these learned constraints as a guide when making decisions in an online setting while still being reactive to reward feedback. To define this agent, we propose to adopt a novel extension to the classical contextual multi-armed bandit setting and we provide a new algorithm called Behavior Constrained Thompson Sampling (BCTS) that allows for online learning while obeying exogenous constraints. Our agent learns a constrained policy that implements the observed behavioral constraints demonstrated by a teacher agent, and then uses this constrained policy to guide the reward-based online exploration and exploitation. We characterize the upper bound on the expected regret of the contextual bandit algorithm that underlies our agent and provide a case study with real world data in two application domains. Our experiments show that the designed agent is able to act within the set of behavior constraints without significantly degrading its overall reward performance.Comment: 9 pages, 6 figure

2009 Celebration of Inquiry Program

8th Celebration of Inquiry, February 11-13, 2009. Theme: Sharing Stories: Learning Through Discovery to Build a Better World. 1st Annual Undergraduate Research Competition abstracts and schedule are included in the program.https://digitalcommons.coastal.edu/inquiry/1007/thumbnail.jp

Heuristic algorithms for solving a class of multiobjective zero-one programming problems

Master'sMASTER OF ENGINEERIN