Todd Easton

Multi-criteria group consensus under linear cost opinion elasticity

Consensus is a pivotal concept in group decision making. Many times, such a consensus is achieved by the experts shifting their opinion towards a point of mutual consent. Such a shift in many cases is the result of laborious negotiations, which escalates the cost of reaching the consensus. Moreover, many times the group decision is multi-criteria oriented in which the experts need to agree on each criterion separately. This paper describes three problems where experts of unequal importance and with a linear cost of changing their opinion (opinion elasticity) consider a single and a multi-criteria decision consensus. These problems achieve a minimum cost consensus without a budget limit. It turns out that the optimal consensus point is at the median opinion for rectilinear cost function and at the weighted average opinion for squared geometric distance calculations. Linear-time algorithms are presented for all cost consensus problems with no budget limits. Proofs, computational complexity and examples are provided for these algorithms.

Minimum Cost Consensus With Quadratic Cost Functions

Group consensus is an important method for making business decisions. In this paper, the consensus process is defined as a dynamic and interactive group decision process, which is coordinated by a moderator who helps the experts to gradually move their opinions closer to each other. This paper describes the importance of group consensus and the need to minimize the cost of this process. Furthermore, this paper describes the costs associated with decision making using group consensus and then describes three methods of reaching consensus assuming quadratic costs for a single-criterion decision problem. The first method finds the group opinion (consensus) that yields the minimum cost of reaching throughout the group. The second method finds the opinion with the minimum cost of the consensus provided that all experts must be within a given distance of the group opinion. The last method finds the maximum number of experts that can fit within the consensus, given a specified budget constraint.

Intelligent Dispatch for Distributed Renewable Resources

Time of use (TOU) pricing is considered by many to be a key part of creating a more energy-efficient and renewable-energy-friendly grid. TOU pricing is also an integral part of the smart grid and is already available to customers of some electric utilities. With TOU pricing becoming a reality, intelligent dispatching systems that utilize energy storage devices (ESDs) to maximize the use of renewable resources, such as energy produced by small, customer owned wind generators and roof-top solar generators, and grid energy while determining the most economic dispatch schedule could play an important role for both the customer and the utility. The purpose of this work is to create an algorithm upon which these dispatching systems can be based. The details of one proposed algorithm are presented. Several case studies are presented to show the effectiveness of the algorithm from both a technical standpoint and an economic standpoint. The case studies show that while the algorithm developed is successful from a technical standpoint, the high cost of energy storage at this time limits its widespread deployment.

Epidemic spreading on weighted contact networks

The study of epidemics is a crucial issue to several areas. An epidemic can have devastating economic and social consequences. A single crop disease in Kansas could destroy the yearly income of many farmers. Previous work using graph theory has determined a universal epidemic threshold found in the graph topology for a binary contact network in the compartmental susceptible-infected (SI) analysis. We expand this threshold to a more realistic measure. A binary uniform level of contact within a society is too idealistic and an improved threshold is found in allowing a spectrum of contact within a contact network. The expanded contact network also allows for asymmetric contact such as a mother caring for her child. Further study in this area should lead to improved simulators, disease modeling, policies and control of infectious diseases and viruses.

Facets of the independent set polytope

Abstract.Theoretical results pertaining to the independent set polytope PISP=conv{x{0,1}n:Ax≤b} are presented. A conflict hypergraph is constructed based on the set of dependent sets which facilitates the examination of the facial structure of PISP. Necessary and sufficient conditions are provided for every nontrivial 0-1 facet-defining inequalities of PISP in terms of hypercliques. The relationship of hypercliques and some classes of knapsack facet-defining inequalities are briefly discussed. The notion of lifting is extended to the conflict hypergraph setting to obtain strong valid inequalities, and back-lifting is introduced to strengthen cut coefficients. Preliminary computational results are presented to illustrate the usefulness of the theoretical findings.

Efficient mitigation strategies for epidemics in rural regions.

Containing an epidemic at its origin is the most desirable mitigation. Epidemics have often originated in rural areas, with rural communities among the first affected. Disease dynamics in rural regions have received limited attention, and results of general studies cannot be directly applied since population densities and human mobility factors are very different in rural regions from those in cities. We create a network model of a rural community in Kansas, USA, by collecting data on the contact patterns and computing rates of contact among a sampled population. We model the impact of different mitigation strategies detecting closely connected groups of people and frequently visited locations. Within those groups and locations, we compare the effectiveness of random and targeted vaccinations using a Susceptible-Exposed-Infected-Recovered compartmental model on the contact network. Our simulations show that the targeted vaccinations of only 10% of the sampled population reduced the size of the epidemic by 34.5%. Additionally, if 10% of the population visiting one of the most popular locations is randomly vaccinated, the epidemic size is reduced by 19%. Our results suggest a new implementation of a highly effective strategy for targeted vaccinations through the use of popular locations in rural communities.

On completing latin squares

Abstract In 1984, Colbourn proved that completing a partially filled latin square is NP -complete. In this paper, we tighten the Colbourn result by showing that completing a partially filled square remains hard even if no more than three unfilled cells exist in any row or column of the square and where only three integers are available.

Optimal topology design for overlay networks

Overlay topology design has been one of the most challenging research areas over the past few years. In this paper, we consider the problem of finding the overlay topology that minimizes a cost function which takes into account the overlay link creation cost and the routing cost. First, we formulate the problem as an Integer Linear Programming (ILP) given a traffic matrix in case of cooperative and non cooperative node behavior. Then, we propose some heuristics to find near-optimal overlay topologies with a reduced complexity. The solutions of the ILP problem in average-size networks have been analyzed, showing that the traffic demands between the nodes affects the decision of creating new overlay links. The heuristics are also compared through extensive numerical evaluation, and guidelines for the selection of the best heuristic as a function of the cost parameters are also provided.

Simultaneously lifting sets of binary variables into cover inequalities for knapsack polytopes

Cover inequalities are commonly used cutting planes for the 0-1 knapsack problem. This paper describes a linear-time algorithm (assuming the knapsack is sorted) to simultaneously lift a set of variables into a cover inequality. Conditions for this process to result in valid and facet-defining inequalities are presented. In many instances, the resulting simultaneously lifted cover inequality cannot be obtained by sequentially lifting over any cover inequality. Some computational results demonstrate that simultaneously lifted cover inequalities are plentiful, easy to find and can be computationally beneficial.

Novel evolutionary models and applications to sequence alignment problems

In this paper, we present a novel graph-theoretical approach for representing a wide variety of sequence analysis problems within a single model. The model allows incorporation of the operations “insertion”, “deletion”, and “substitution”, and various parameters such as relative distances and weights. Conceptually, we refer the problem as the minimum weight common mutated sequence (MWCMS) problem. The MWCMS model has many applications including multiple sequence alignment problem, the phylogenetic analysis, the DNA sequencing problem, and sequence comparison problem, which encompass a core set of very difficult problems in computational biology. Thus the model presented in this paper lays out a mathematical modeling framework that allows one to investigate theoretical and computational issues, and to forge new advances for these distinct, but related problems.Through the introduction of supernodes, and the multi-layer supergraph, we proved that MWCMS is