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Craig Tovey

Georgia Institute of Technology, Industrial and Systems Engineering, Faculty Member

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I do pure, applied, and interdisciplinary research from a basis in algorithms, discrete mathematics, probability, optimization, and general knowledge. I've developed and applied methods to process planning for circuit board assembly, mortgage pooling, cellular phone frequency assignment, web host server allocation, robot motion planning, etc. My interdisciplinary work includes computational social choice, animal dominance, spatial voting, fire ant structures, epidemiology. My current primary focus is on political analytics.
Supervisors: George Dantzig

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Prof. Saeid Eslamian

Isfahan University of Technology

David Pierre Leibovitz

Carleton University

The University of New South Wales

Ellips Masehian

California State Polytechnic University at Pomona

ISCTE - University Institute of Lisbon (ISCTE-IUL)

University of Melbourne

Kansas State University

Cleveland Clinic

University of Cologne

Wesley Holliday

University of California, Berkeley

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Papers by Craig Tovey

How Hard is It to Control en Election?

An Improved Algorithm and Analysis for Finding the Simpson Point of a Convex Polygon In Competitive Location

by Joy Bhadury and Craig Tovey

We consider the problem of finding the Simpson Point, also known as the (1|1) Centroid, of a mark... more We consider the problem of finding the Simpson Point, also known as the (1|1) Centroid, of a market that is uniformly distributed over a convex polygon. Diaz and O'Rourke (1994) developed an iterati ve search algorithm for the case when the demand distribution is uniform; they also observed that it did not appear to converge pointwise, and modified it to

Dynamic and stochastic resource minimization

We consider a problem where tasks arrive randomly over time, and all tasks have to be performed u... more We consider a problem where tasks arrive randomly over time, and all tasks have to be performed using reusable resources before a given deadline. The objective is to minimize the total cost of the operation by minimizing the number of resources used. Two cases are considered: first the case in which we have no information on future tasks, and then the case in which we know the probability distribution of future tasks. Sub-optimal and optimal policies are analyzed for the two cases. Keywords: Resource allocation, Worst-case analysis, Stochastic dynamic programming 1 Introduction We study an optimization problem concerned with the optimal allocation of scarce resources to tasks over time. Key characteristics of an optimization problem are the assumptions about the availability of information, both regarding the information content and the time the information becomes available to a decision maker. In deterministic problems all relevant data are assumed to be known before any decisions a...

Multi-Agent Path Finding with Payload Transfers and the Package-Exchange Robot-Routing Problem

Proceedings of the AAAI Conference on Artificial Intelligence

We study transportation problems where robots have to deliver packages and can transfer the packa... more We study transportation problems where robots have to deliver packages and can transfer the packages among each other. Specifically, we study the package-exchange robot-routing problem (PERR), where each robot carries one package, any two robots in adjacent locations can exchange their packages, and each package needs to be delivered to a given destination. We prove that exchange operations make all PERR instances solvable. Yet, we also show that PERR is NP-hard to approximate within any factor less than 4/3 for makespan minimization and is NP-hard to solve for flowtime minimization, even when there are only two types of packages. Our proof techniques also generate new insights into other transportation problems, for example, into the hardness of approximating optimal solutions to the standard multi-agent path-finding problem (MAPF). Finally, we present optimal and suboptimal PERR solvers that are inspired by MAPF solvers, namely a flow-based ILP formulation and an adaptation of con...

Probabilistic Copeland Tournaments

adaptive agents and multi-agents systems, May 4, 2015

Supplementary Movie S1 from Fire ants perpetually rebuild sinking towers

Time lapse video of ant tower construction around rods of diameter 6.4 mm and 11.2 mm. Video is s... more

Shape Data AntTower from Fire ants perpetually rebuild sinking towers

In the aftermath of a flood, fire ants, <i>Solenopsis invicta</i>, cluster into tempo... more In the aftermath of a flood, fire ants, <i>Solenopsis invicta</i>, cluster into temporary encampments. The encampments can contain hundreds of thousands of ants and reach over 30 ants high. How do ants build such tall structures without being crushed? In this combined experimental and theoretical study, we investigate the shape and rate of construction of ant towers around a central support. The towers are bell shaped, consistent with towers of constant strength such as the Eiffel tower, where each element bears an equal load. However, unlike the Eiffel tower, the ant tower is built through a process of trial and error, whereby failed portions avalanche until the final shape emerges. High-speed and novel X-ray videography reveal that the tower constantly sinks and is rebuilt, reminiscent of large multicellular systems such as human skin. We combine the behavioural rules that produce rafts on water with measurements of adhesion and attachment strength to model the rate of...

Supplementary Movie S3 from Fire ants perpetually rebuild sinking towers

A finger of ants peels off the central rod, indicating the importance of ring formation in making... more

Supplementary Movie S5 from Fire ants perpetually rebuild sinking towers

Time lapse video of the bottom of an ant tower. Ants form tunnels throughout the building process... more

Overview: Generalizations of Multi-Agent Path Finding to Real-World Scenarios

ArXiv, 2017

Multi-agent path finding (MAPF) is well-studied in artificial intelligence, robotics, theoretical... more Multi-agent path finding (MAPF) is well-studied in artificial intelligence, robotics, theoretical computer science and operations research. We discuss issues that arise when generalizing MAPF methods to real-world scenarios and four research directions that address them. We emphasize the importance of addressing these issues as opposed to developing faster methods for the standard formulation of the MAPF problem.

aversal Algorithm MCM Substrate

single probe to test MCA4 interconnects is presented. The goal of this work is to optimize the to... more single probe to test MCA4 interconnects is presented. The goal of this work is to optimize the total distance traveled by a single test probe on an MCM substrate and thereby reduce the substrate testing time. It is assumed that only one terminal pad of each interconnection net is to be probed. Our algorithm is based on tour construction and improvement with arbitrary insertion for solving a complex variation of the traveling salesman problem. improved insertion and shuJj?ing techniques guarantee the step by step optimization of the total traversal cost. The valid@ of the algorithm has been confirmed with experiments and shows that up to 50% reduction in probe traversal time can be obtained with our technique.

Conditions for Stability in Strategic Matching

We consider the stability of matchings when individuals strategically submit preference informati... more We consider the stability of matchings when individuals strategically submit preference information to a publicly known algorithm. Most pure Nash equilibria of the ensuing game yield a matching that is unstable with respect to the individuals’ sincere preferences. We introduce a wellsupported minimal dishonesty constraint, and obtain conditions under which every pure Nash equilibrium yields a matching that is stable with respect to the sincere preferences. The conditions on the matching algorithm are to be either fully-randomized, or monotonic and independent of non-spouses (INS), an IIA-like property. These conditions are significant because they support the use of algorithms other than the Gale-Shapley (man-optimal) algorithm for kidney exchange and other applications. We prove that the Gale-Shapley algorithm always yields the woman-optimal matching when individuals are minimally dishonest. However, we give a negative answer to one of Gusfield and Irving’s open questions: there is...

The Price of Deception in Spatial Social Choice

Except for a few strategy-proof mechanisms on the real line, spatial social choice mechanisms are... more Except for a few strategy-proof mechanisms on the real line, spatial social choice mechanisms are usually manipulable. But is it wise to treat all manipulations as equally bad? We introduce a new measure, the price of deception, to make finer distinctions than between “strategy-proof” and “manipulable.” The price of deception, akin to but distinct from the price of anarchy in computer science, measures how much strategic behavior can alter the cost of the social choice. We propose it should be one of the criteria by which a selection rule is assessed. Supported by experimental economics data, our measure employs a novel minimal dishonesty criterion to refine the set of Nash equilibria. We calculate the price of deception for standard spatial selection rules, including 1-Median and 1-Mean, and find significant differences among them. We also find that a mechanism designer can significantly lessen the impact of manipulation by altering the set of allowed points to a hyperrectangle. Th...

Towards Completely Decentralized Mustering for StarCraft

We study decentralized agent coordination with performance guarantees by developing a primitive f... more

Large-scale neuroanatomy using LASSO: Loop-based Automated Serial Sectioning Operation

PloS one, 2018

Serial section transmission electron microscopy (ssTEM) is the most promising tool for investigat... more Serial section transmission electron microscopy (ssTEM) is the most promising tool for investigating the three-dimensional anatomy of the brain with nanometer resolution. Yet as the field progresses to larger volumes of brain tissue, new methods for high-yield, low-cost, and high-throughput serial sectioning are required. Here, we introduce LASSO (Loop-based Automated Serial Sectioning Operation), in which serial sections are processed in "batches." Batches are quantized groups of individual sections that, in LASSO, are cut with a diamond knife, picked up from an attached waterboat, and placed onto microfabricated TEM substrates using rapid, accurate, and repeatable robotic tools. Additionally, we introduce mathematical models for ssTEM with respect to yield, throughput, and cost to access ssTEM scalability. To validate the method experimentally, we processed 729 serial sections of human brain tissue (~40 nm x 1 mm x 1 mm). Section yield was 727/729 (99.7%). Sections were ...

Optimal solution to the multinomial selection problem for two alternatives

Sequential Analysis, 2017

ABSTRACT The multinomial selection problem is to find a stopping policy for repeated independent ... more ABSTRACT The multinomial selection problem is to find a stopping policy for repeated independent trials, each of which reports a winner among competing alternatives that has low expected cost and high probability of correct selection (PCS) of the best alternative. In 1959, Bechhofer, Elmaghraby, and Morse formulated the problem as minimizing the worst-case expected number of trials, subject to a lower bound on PCS and upper bound on the maximum number of trials, over all probability vectors outside an indifference zone. For the case of two alternatives, we prove that if one employs a particular probability vector known as the slippage configuration, then a linear program always finds an optimal stopping policy.

In defense of basic research

Science, 2017

A 1939 essay resonates today, persuasively advocating for science for science's sake

Smallest tournaments not realizable by [FORMULA]-majority voting

Social Choice and Welfare, 2009

The finagle point and the epsilon-core: A comment on Br�uninger's proof

Circuit partitioning via set partitoning and column generation

Operations Research, 1996

How Hard is It to Control en Election?

An Improved Algorithm and Analysis for Finding the Simpson Point of a Convex Polygon In Competitive Location

by Joy Bhadury and Craig Tovey

We consider the problem of finding the Simpson Point, also known as the (1|1) Centroid, of a mark... more We consider the problem of finding the Simpson Point, also known as the (1|1) Centroid, of a market that is uniformly distributed over a convex polygon. Diaz and O'Rourke (1994) developed an iterati ve search algorithm for the case when the demand distribution is uniform; they also observed that it did not appear to converge pointwise, and modified it to

Dynamic and stochastic resource minimization

We consider a problem where tasks arrive randomly over time, and all tasks have to be performed u... more We consider a problem where tasks arrive randomly over time, and all tasks have to be performed using reusable resources before a given deadline. The objective is to minimize the total cost of the operation by minimizing the number of resources used. Two cases are considered: first the case in which we have no information on future tasks, and then the case in which we know the probability distribution of future tasks. Sub-optimal and optimal policies are analyzed for the two cases. Keywords: Resource allocation, Worst-case analysis, Stochastic dynamic programming 1 Introduction We study an optimization problem concerned with the optimal allocation of scarce resources to tasks over time. Key characteristics of an optimization problem are the assumptions about the availability of information, both regarding the information content and the time the information becomes available to a decision maker. In deterministic problems all relevant data are assumed to be known before any decisions a...

Multi-Agent Path Finding with Payload Transfers and the Package-Exchange Robot-Routing Problem

Proceedings of the AAAI Conference on Artificial Intelligence

We study transportation problems where robots have to deliver packages and can transfer the packa... more We study transportation problems where robots have to deliver packages and can transfer the packages among each other. Specifically, we study the package-exchange robot-routing problem (PERR), where each robot carries one package, any two robots in adjacent locations can exchange their packages, and each package needs to be delivered to a given destination. We prove that exchange operations make all PERR instances solvable. Yet, we also show that PERR is NP-hard to approximate within any factor less than 4/3 for makespan minimization and is NP-hard to solve for flowtime minimization, even when there are only two types of packages. Our proof techniques also generate new insights into other transportation problems, for example, into the hardness of approximating optimal solutions to the standard multi-agent path-finding problem (MAPF). Finally, we present optimal and suboptimal PERR solvers that are inspired by MAPF solvers, namely a flow-based ILP formulation and an adaptation of con...

Probabilistic Copeland Tournaments

adaptive agents and multi-agents systems, May 4, 2015

Supplementary Movie S1 from Fire ants perpetually rebuild sinking towers

Time lapse video of ant tower construction around rods of diameter 6.4 mm and 11.2 mm. Video is s... more

Shape Data AntTower from Fire ants perpetually rebuild sinking towers

In the aftermath of a flood, fire ants, <i>Solenopsis invicta</i>, cluster into tempo... more In the aftermath of a flood, fire ants, <i>Solenopsis invicta</i>, cluster into temporary encampments. The encampments can contain hundreds of thousands of ants and reach over 30 ants high. How do ants build such tall structures without being crushed? In this combined experimental and theoretical study, we investigate the shape and rate of construction of ant towers around a central support. The towers are bell shaped, consistent with towers of constant strength such as the Eiffel tower, where each element bears an equal load. However, unlike the Eiffel tower, the ant tower is built through a process of trial and error, whereby failed portions avalanche until the final shape emerges. High-speed and novel X-ray videography reveal that the tower constantly sinks and is rebuilt, reminiscent of large multicellular systems such as human skin. We combine the behavioural rules that produce rafts on water with measurements of adhesion and attachment strength to model the rate of...

Supplementary Movie S3 from Fire ants perpetually rebuild sinking towers

A finger of ants peels off the central rod, indicating the importance of ring formation in making... more

Supplementary Movie S5 from Fire ants perpetually rebuild sinking towers

Time lapse video of the bottom of an ant tower. Ants form tunnels throughout the building process... more

Overview: Generalizations of Multi-Agent Path Finding to Real-World Scenarios

ArXiv, 2017

Multi-agent path finding (MAPF) is well-studied in artificial intelligence, robotics, theoretical... more Multi-agent path finding (MAPF) is well-studied in artificial intelligence, robotics, theoretical computer science and operations research. We discuss issues that arise when generalizing MAPF methods to real-world scenarios and four research directions that address them. We emphasize the importance of addressing these issues as opposed to developing faster methods for the standard formulation of the MAPF problem.

aversal Algorithm MCM Substrate

single probe to test MCA4 interconnects is presented. The goal of this work is to optimize the to... more single probe to test MCA4 interconnects is presented. The goal of this work is to optimize the total distance traveled by a single test probe on an MCM substrate and thereby reduce the substrate testing time. It is assumed that only one terminal pad of each interconnection net is to be probed. Our algorithm is based on tour construction and improvement with arbitrary insertion for solving a complex variation of the traveling salesman problem. improved insertion and shuJj?ing techniques guarantee the step by step optimization of the total traversal cost. The valid@ of the algorithm has been confirmed with experiments and shows that up to 50% reduction in probe traversal time can be obtained with our technique.

Conditions for Stability in Strategic Matching

We consider the stability of matchings when individuals strategically submit preference informati... more We consider the stability of matchings when individuals strategically submit preference information to a publicly known algorithm. Most pure Nash equilibria of the ensuing game yield a matching that is unstable with respect to the individuals’ sincere preferences. We introduce a wellsupported minimal dishonesty constraint, and obtain conditions under which every pure Nash equilibrium yields a matching that is stable with respect to the sincere preferences. The conditions on the matching algorithm are to be either fully-randomized, or monotonic and independent of non-spouses (INS), an IIA-like property. These conditions are significant because they support the use of algorithms other than the Gale-Shapley (man-optimal) algorithm for kidney exchange and other applications. We prove that the Gale-Shapley algorithm always yields the woman-optimal matching when individuals are minimally dishonest. However, we give a negative answer to one of Gusfield and Irving’s open questions: there is...

The Price of Deception in Spatial Social Choice

Except for a few strategy-proof mechanisms on the real line, spatial social choice mechanisms are... more Except for a few strategy-proof mechanisms on the real line, spatial social choice mechanisms are usually manipulable. But is it wise to treat all manipulations as equally bad? We introduce a new measure, the price of deception, to make finer distinctions than between “strategy-proof” and “manipulable.” The price of deception, akin to but distinct from the price of anarchy in computer science, measures how much strategic behavior can alter the cost of the social choice. We propose it should be one of the criteria by which a selection rule is assessed. Supported by experimental economics data, our measure employs a novel minimal dishonesty criterion to refine the set of Nash equilibria. We calculate the price of deception for standard spatial selection rules, including 1-Median and 1-Mean, and find significant differences among them. We also find that a mechanism designer can significantly lessen the impact of manipulation by altering the set of allowed points to a hyperrectangle. Th...

Towards Completely Decentralized Mustering for StarCraft

We study decentralized agent coordination with performance guarantees by developing a primitive f... more

Large-scale neuroanatomy using LASSO: Loop-based Automated Serial Sectioning Operation

PloS one, 2018

Serial section transmission electron microscopy (ssTEM) is the most promising tool for investigat... more Serial section transmission electron microscopy (ssTEM) is the most promising tool for investigating the three-dimensional anatomy of the brain with nanometer resolution. Yet as the field progresses to larger volumes of brain tissue, new methods for high-yield, low-cost, and high-throughput serial sectioning are required. Here, we introduce LASSO (Loop-based Automated Serial Sectioning Operation), in which serial sections are processed in "batches." Batches are quantized groups of individual sections that, in LASSO, are cut with a diamond knife, picked up from an attached waterboat, and placed onto microfabricated TEM substrates using rapid, accurate, and repeatable robotic tools. Additionally, we introduce mathematical models for ssTEM with respect to yield, throughput, and cost to access ssTEM scalability. To validate the method experimentally, we processed 729 serial sections of human brain tissue (~40 nm x 1 mm x 1 mm). Section yield was 727/729 (99.7%). Sections were ...

Optimal solution to the multinomial selection problem for two alternatives

Sequential Analysis, 2017

ABSTRACT The multinomial selection problem is to find a stopping policy for repeated independent ... more ABSTRACT The multinomial selection problem is to find a stopping policy for repeated independent trials, each of which reports a winner among competing alternatives that has low expected cost and high probability of correct selection (PCS) of the best alternative. In 1959, Bechhofer, Elmaghraby, and Morse formulated the problem as minimizing the worst-case expected number of trials, subject to a lower bound on PCS and upper bound on the maximum number of trials, over all probability vectors outside an indifference zone. For the case of two alternatives, we prove that if one employs a particular probability vector known as the slippage configuration, then a linear program always finds an optimal stopping policy.

In defense of basic research

Science, 2017

A 1939 essay resonates today, persuasively advocating for science for science's sake

Smallest tournaments not realizable by [FORMULA]-majority voting

Social Choice and Welfare, 2009

The finagle point and the epsilon-core: A comment on Br�uninger's proof

Circuit partitioning via set partitoning and column generation

Operations Research, 1996