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42
Fast approximate energy minimization via graph cuts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when v ..."
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Cited by 1485 (54 self)
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In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed. The first move we consider is an αβswap: for a pair of labels α, β, this move exchanges the labels between an arbitrary set of pixels labeled α and another arbitrary set labeled β. Our first algorithm generates a labeling such that there is no swap move that decreases the energy. The second move we consider is an αexpansion: for a label α, this move assigns an arbitrary set of pixels the label α. Our second
An Explicit Lower Bound for TSP with Distances One and Two
 Proc. 16th STACS (1999), LNCS 1563
, 1999
"... . We show that it is, for any #>0, NPhard to approximate the asymmetric traveling salesman problem with distances one and two within 2805/2804  #. For the special case where the distance function is constrained to be symmetric, we show a lower bound of 5381/5380  #,for any #>0. Whil ..."
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Cited by 21 (2 self)
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. We show that it is, for any #>0, NPhard to approximate the asymmetric traveling salesman problem with distances one and two within 2805/2804  #. For the special case where the distance function is constrained to be symmetric, we show a lower bound of 5381/5380  #,for any #>0. While it was previously known that there exists some constant, strictly greater than one, such that it is NPhard to approximate the traveling salesman problem with distances one and two within that constant, this result is a first step towards the establishment of a good bound. In our proof, we develop a new gadget construction to reduce from systems of linear equations mod 2 with two unknowns in each equation and at most three occurrences of each variable. Compared with earlier reductions to the traveling salesman problem with distances one and two, ours reduces the number of cities to less than a tenth of what was previously necessary. Key words. The traveling salesman problem, Approximabi...
TSP  Infrastructure for the Traveling Salesperson Problem
 JOURNAL OF STATISTICAL SOFTWARE
, 2006
"... The traveling salesperson or salesman problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP ..."
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Cited by 12 (2 self)
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The traveling salesperson or salesman problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP is difficult since it belongs to the class of NPcomplete problems. The importance of the TSP arises besides from its theoretical appeal from the variety of its applications. In addition to vehicle routing, many other applications, e.g., computer wiring, cutting wallpaper, job sequencing or several data visualization techniques, require the solution of a TSP. In this paper we introduce the R package TSP which provides a basic infrastructure for handling and solving the traveling salesperson problem. The package features S3 classes for specifying a TSP and its (possibly optimal) solution as well as several heuristics to find good solutions. In addition, it provides an interface to Concorde, one of the best exact TSP solvers currently available.
degrees in electrical engineering from The
 Ohio State University
, 1980
"... From its roots in physics, mathematics, and biology, the study of complexity science, or complex adaptive systems, has expanded into the domain of organizations and systems of organizations. Complexity science is useful for studying the evolution of complex organizations entities with multiple, di ..."
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From its roots in physics, mathematics, and biology, the study of complexity science, or complex adaptive systems, has expanded into the domain of organizations and systems of organizations. Complexity science is useful for studying the evolution of complex organizations entities with multiple, diverse, interconnected elements. Evolution of complex organizations often is accompanied by feedback effects, nonlinearity, and other conditions that add to the complexity of existing organizations and the unpredictability of the emergence of new entities. Health care organizations are an ideal setting for the application of complexity science due to the diversity of organizational forms and interactions among organizations that are evolving. Too, complexity science can benefit from attention to the world’s most complex human organizations. Organizations within and across the health care sector are increasingly interdependent. Not only are new, highly powerful and diverse organizational forms being created, but also the restructuring has occurred within very short periods of time. In this chapter, we review the basic tenets of complexity science. We identify a
A Multiobjective Optimization Approach to Urban School Bus Routing : Formulation and Solution Method
 Transportation Research: Part A, Policy and Practice
, 1995
"... This paper considers the case of providing school bus transportation in urban areas and does not deal with school bus routing in rural areas. Amultiobjective mathematicalformulation is presented for the Urban School Bus Routing Problem (USBRP). A heuristic algorithm based on this formulation is deve ..."
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Cited by 9 (0 self)
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This paper considers the case of providing school bus transportation in urban areas and does not deal with school bus routing in rural areas. Amultiobjective mathematicalformulation is presented for the Urban School Bus Routing Problem (USBRP). A heuristic algorithm based on this formulation is developed and tested with data from a sample school board location in Wellington County. Since school bus services in Ontario are funded through local property taxes in conjunction with grants from the provincial Ministry of Education, and since the service involves considerations of efficiency (cost minimization) and user equity (fairness), the evaluation criteria for measuring the appropriateness of school bus routes are inherently multiobjective in nature. In this paper we present a multiobjective mathematical formulation for SBRP in urban areas, develop a heuristic algorithm based on this formulation, and report results of testing this algorithm on sample data from the Wellington Country Board of Education. In the next section the criteria that are used to assess the performance of solutions to the USBRP are discussed. Performance Criteria for the Provision of School Bus Transportation Services
Modeling highresolution broadband discourse in complex adaptive systems
 Nonlinear Dynamics, Psychology, & Life Sciences
, 2003
"... Numerous researchers and practitioners have turned to complexity science to better understand human systems. Simulation can be used to observe how the microlevel actions of many human agents create emergent structures and novel behavior in complex adaptive systems. In such simulations, communication ..."
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Cited by 8 (2 self)
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Numerous researchers and practitioners have turned to complexity science to better understand human systems. Simulation can be used to observe how the microlevel actions of many human agents create emergent structures and novel behavior in complex adaptive systems. In such simulations, communication between human agents is often modeled simply as message passing, where a message or text may transfer data, trigger action, or inform context. Human communication involves more than the transmission of texts and messages, however. Such a perspective is likely to limit the effectiveness and insight that we can gain from simulations, and complexity science itself. In this paper, we propose a model of how close analysis of discursive processes between individuals (highresolution), which occur simultaneously across a human system (broadband), dynamically evolve. We propose six different processes that describe how evolutionary variation can occur in texts— recontextualization, pruning, chunking, merging, appropriation, and mutation. These process models can facilitate the simulation of highresolution, broadband discourse processes, and can aid in the analysis of data from such processes. Examples are used to illustrate each process. We make the tentative suggestion that discourse may evolve to the “edge of chaos. ” We conclude with a discussion concerning how highresolution, broadband discourse data could actually be collected. KEY WORDS: broadband discourse; communication; selforganization; complex adaptive system.
Finding low cost TSP and 2matching solutions using certain halfinteger subtour vertices
, 1998
"... Consider the traveling salesman problem (TSP) defined on the complete graph, where the edge costs satisfy the triangle inequality. Let TOUR denote the optimal solution value for the TSP. Two well known relaxations of the TSP are the subtour elimination problem and the 2matching problem. If we let S ..."
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Cited by 6 (3 self)
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Consider the traveling salesman problem (TSP) defined on the complete graph, where the edge costs satisfy the triangle inequality. Let TOUR denote the optimal solution value for the TSP. Two well known relaxations of the TSP are the subtour elimination problem and the 2matching problem. If we let SUBT and 2M represent the optimal solution values for these two relaxations, then it has been conjectured that TOUR/SUBT ≤ 4/3, and that 2M/SUBT ≤ 10/9. In this paper we exploit the structure of certain 1/2integer solutions for the subtour elimination problem in order to obtain low cost TSP and 2matching solutions. In particular, we show that for cost functions for which the optimal subtour elimination solutions fall into our classes, the above two conjectures are true. We also discuss how this class of subtour elimination solutions is important for the potential resolution of the 4/3 conjecture above. Our proofs are constructive and could be implemented in polynomial time, and thus for such cost functions provide a 4/3 (or better) approximation algorithm for the TSP. Key words: traveling salesman problem, subtour elimination problem, 2matching, approximation algorithm. 1
Finding the exact integrality gap for small travelling salesman problems
 Math. of Operations Research
, 2002
"... Abstract. The Symmetric Travelling Salesman Problem (STSP) is to find a minimum weight Hamiltonian cycle in a weighted complete graph on n nodes. One direction which seems promising for finding improved solutions for the STSP is the study of a linear relaxation of this problem called the Subtour Eli ..."
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Cited by 5 (3 self)
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Abstract. The Symmetric Travelling Salesman Problem (STSP) is to find a minimum weight Hamiltonian cycle in a weighted complete graph on n nodes. One direction which seems promising for finding improved solutions for the STSP is the study of a linear relaxation of this problem called the Subtour Elimination Problem (SEP). A well known conjecture in combinatorial optimization says that the integrality gap of the SEP is 4/3 in the metric case. Currently the best upper bound known for this integrality gap is 3/2. Finding the exact value for the integrality gap for the SEP is difficult even for small values of n due to the exponential size of the data involved. In this paper we describe how we were able to overcome such difficulties and obtain the exact integrality gap for all values of n up to 10. Our results give a verification of the 4/3 conjecture for small values of n, and also give rise to a new stronger form of the conjecture which is dependent on n. 1
Hamilton Circuits in Hexagonal Grid Graphs
, 2007
"... We look at a variant of the Hamilton circuit problem, where the input is restricted to hexagonal grid graphs. A hexagonal grid graph has a vertex set that is a subset of the grid points of a regular hexagonal tiling of the plane and edges corresponding to hexagon sides. We show that Hamilton circuit ..."
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Cited by 3 (1 self)
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We look at a variant of the Hamilton circuit problem, where the input is restricted to hexagonal grid graphs. A hexagonal grid graph has a vertex set that is a subset of the grid points of a regular hexagonal tiling of the plane and edges corresponding to hexagon sides. We show that Hamilton circuit in hexagonal grid graphs is NPcomplete.
Microsoft Visual Studio. Version DotNet. http://msdn.microsoft.com/vstudio
 Computing in Science and Engineering
, 2002
"... The theory of computational complexity has some interesting links to physics, in particular to quantum computing and statistical mechanics. This article contains an informal introduction to this theory and its links to physics. ..."
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Cited by 2 (0 self)
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The theory of computational complexity has some interesting links to physics, in particular to quantum computing and statistical mechanics. This article contains an informal introduction to this theory and its links to physics.