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37
A simultaneous parametric maximumflow algorithm for finding the complete . . .
, 2005
"... A natural extension of the maximum flow problem is the parametric maximum flow problem, in which some of the arc capacities in the network are functions of a single parameter λ. Previous approaches to the problem compute the maximum flow for a given sequence of parameter values sequentially taking ..."
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A natural extension of the maximum flow problem is the parametric maximum flow problem, in which some of the arc capacities in the network are functions of a single parameter λ. Previous approaches to the problem compute the maximum flow for a given sequence of parameter values sequentially taking advantage of the solution at the previous parameter value to speed up the computation at the next. In this paper, we present a new Simultaneous Parametric Maximum Flow (SPMF) algorithm that finds the maximum flow and a minimum cut of an important class of parametric networks for all values of parameter λ simultaneously. Instead of working with the original parametric network, a new nonparametric network is derived from the original and the SPMF gives a particular state of the flows in the derived network, from which the nested minimumcuts under all λvalues are derived in a single scan of the vertices in a sorted order. SPMF simultaneously discovers all breakpoints of λ where the maximum flow as a stepfunction of λ jumps. The maximum flows at these λvalues are calculated in O(m) time from the minimumcuts; m is the number of arcs. Generalization beyond bipartite networks is also shown.
Cost Evaluation of Soft Global Constraints
 Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, volume 3011 of LNCS
, 2004
"... Abstract. This paper shows that existing definitions of costs associated with soft global constraints are not sufficient to deal with all the usual global constraints. We propose more expressive definitions: refined variablebased cost, objectbased cost and graph properties based cost. For the first ..."
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Abstract. This paper shows that existing definitions of costs associated with soft global constraints are not sufficient to deal with all the usual global constraints. We propose more expressive definitions: refined variablebased cost, objectbased cost and graph properties based cost. For the first two ones we provide adhoc algorithms to compute the cost from a complete assignment of values to variables. A representative set of global constraints is investigated. Such algorithms are generally not straightforward and some of them are even NPHard. Then we present the major feature of the graph properties based cost: a systematic way for evaluating the cost with a polynomial complexity. 1
The Geometric Maximum Traveling Salesman Problem
, 1999
"... We consider the traveling salesman problem when the cities are points in R^d for some fixed d and distances are computed according to geometric distances, determined by some norm. We show that for any polyhedral norm, the problem of finding a tour of maximum length can be solved in polynomial time. ..."
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Cited by 6 (3 self)
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We consider the traveling salesman problem when the cities are points in R^d for some fixed d and distances are computed according to geometric distances, determined by some norm. We show that for any polyhedral norm, the problem of finding a tour of maximum length can be solved in polynomial time. If arithmetic operations are assumed to take unit time, our algorithms run in time O(n log n), where f is the number of facets of the polyhedron determining the polyhedral norm. Thus for example we have O(n log n) algorithms for the cases of points in the plane under the Rectilinear and Sup norms. This is in contrast to the fact that finding a minimum length tour in each case is NPhard. Our approach can be extended to the more general case of quasinorms with not necessarily symmetric unit ball, where we get a complexity of O(n log n).
Experimental evaluation of parametric maxflow algorithms
 In WEA ’07: Proceedings of the 6th Workshop on Experimental Algorithms
, 2007
"... Abstract. The parametric maximum flow problem is an extension of the classical maximum flow problem in which the capacities of certain arcs are not fixed but are functions of a single parameter. Gallo et al. [6] showed that certain versions of the pushrelabel algorithm for ordinary maximum flow can ..."
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Abstract. The parametric maximum flow problem is an extension of the classical maximum flow problem in which the capacities of certain arcs are not fixed but are functions of a single parameter. Gallo et al. [6] showed that certain versions of the pushrelabel algorithm for ordinary maximum flow can be extended to the parametric problem while only increasing the worstcase time bound by a constant factor. Recently Zhang et al. [14,13] proposed a novel, simple balancing algorithm for the parametric problem on bipartite networks. They claimed good performance for their algorithm on networks arising from a realworld application. We describe the results of an experimental study comparing the performance of the balancing algorithm, the GGT algorithm, and a simplified version of the GGT algorithm, on networks related to those of the application of Zhang et al. as well as networks designed to be hard for the balancing algorithm. Our implementation of the balancing algorithm beats both versions of the GGT algorithm on networks related to the application, thus supporting the observations of Zhang et al. On the other hand, the GGT algorithm is more robust; it beats the balancing algorithm on some natural networks, and by asymptotically increasing amount on networks designed to be hard for the balancing algorithm. 1
A New Property And A Faster Algorithm For Baseball Elimination
 SIAM Journal on Discrete Mathematics
, 1999
"... . In the baseball elimination problem, there is a league consisting of n teams. At some point during the season, team i has w i wins and g ij games left to play against team j.Ateamis eliminated if it cannot possibly finish the season in first place or tied for first place. The goal is to determine ..."
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Cited by 5 (0 self)
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. In the baseball elimination problem, there is a league consisting of n teams. At some point during the season, team i has w i wins and g ij games left to play against team j.Ateamis eliminated if it cannot possibly finish the season in first place or tied for first place. The goal is to determine exactly which teams are eliminated. The problem is not as easy as many sports writers would have you believe, in part because the answer depends not only on the number of games won and left to play, but also on the schedule of remaining games. In the 1960's, Schwartz showed how to determine whether one particular team is eliminated using a maximum flow computation. This paper indicates that the problem is not as di#cult as many mathematicians would have you believe. For each team i,letg i denote the number of games remaining. We prove that there exists a value W # such that team i is eliminated if and only if w i + g i <W # . Using this surprising fact, we can determine all eliminated team...
Polynomial time algorithms for ratio regions and a variant of normalized cut
 IEEE Trans. Pattern Anal. Mach. Intell
"... Abstract—In partitioning, clustering, and grouping problems, a typical goal is to group together similar objects, or pixels in the case of image processing. At the same time, another goal is to have each group distinctly dissimilar from the rest and possibly to have the group size fairly large. Thes ..."
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Abstract—In partitioning, clustering, and grouping problems, a typical goal is to group together similar objects, or pixels in the case of image processing. At the same time, another goal is to have each group distinctly dissimilar from the rest and possibly to have the group size fairly large. These goals are often combined as a ratio optimization problem. One example of such a problem is a variant of the normalized cut problem, another is the ratio regions problem. We devise here the first polynomial time algorithms solving optimally the ratio region problem and the variant of normalized cut, as well as a few other ratio problems. The algorithms are efficient and combinatorial, in contrast with nonlinear continuous approaches used in the image segmentation literature, which often employ spectral techniques. Such techniques deliver solutions in real numbers which are not feasible to the discrete partitioning problem. Furthermore, these continuous approaches are computationally expensive compared to the algorithms proposed here. The algorithms presented here use as a subroutine a minimum s; tcut procedure on a related graph which is of polynomial size. The output consists of the optimal solution to the respective ratio problem, as well as a sequence of nested solutions with respect to any relative weighting of the objectives of the numerator and denominator. Index Terms—Grouping, image segmentation, graph theoretic methods, partitioning. Ç
TwoLevel PushRelabel Algorithm for the Maximum Flow Problem
"... Abstract. We describe a twolevel pushrelabel algorithm for the maximum flow problem and compare it to the competing codes. The algorithm generalizes a practical algorithm for bipartite flows. Experiments show that the algorithm performs well on several problem families. 1 ..."
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Abstract. We describe a twolevel pushrelabel algorithm for the maximum flow problem and compare it to the competing codes. The algorithm generalizes a practical algorithm for bipartite flows. Experiments show that the algorithm performs well on several problem families. 1
A Fast Algorithm for the Minimax Flow Problem with 0/1 Weights
"... this paper, we define the minimax flow problem and design an O(k \Delta M(n;m)) time optimal algorithm for a special case of the problem in which the weights on arcs are either 0 or 1, where n is the number of vertices, m is the number of arcs, k (where 1 k m) is the number of arcs with nonzero we ..."
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this paper, we define the minimax flow problem and design an O(k \Delta M(n;m)) time optimal algorithm for a special case of the problem in which the weights on arcs are either 0 or 1, where n is the number of vertices, m is the number of arcs, k (where 1 k m) is the number of arcs with nonzero weights, and M(n;m) is the best time bound for finding a maximum flow in a network.
Fast fusion moves for multimodel estimation
 IN: PROCEEDINGS OF THE EUROPEAN CONFERENCE ON COMPUTER VISION
, 2012
"... We develop a fast, effective algorithm for minimizing a wellknown objective function for robust multimodel estimation. Our work introduces a combinatorial step belonging to a family of powerful movemaking methods like αexpansion and fusion. We also show that our subproblem can be quickly transf ..."
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We develop a fast, effective algorithm for minimizing a wellknown objective function for robust multimodel estimation. Our work introduces a combinatorial step belonging to a family of powerful movemaking methods like αexpansion and fusion. We also show that our subproblem can be quickly transformed into a comparatively small instance of minimumweighted vertexcover. In practice, these vertexcover subproblems are almost always bipartite and can be solved exactly by specialized network flow algorithms. Experiments indicate that our approach achieves the robustness of methods like affinity propagation, whilst providing the speed of fast greedy heuristics.
Minimizing Sparse HighOrder Energies by Submodular Vertexcover
, 2012
"... Inference in highorder graphical models has become important in recent years. Several approaches are based, for example, on generalized messagepassing, or on transformation to a pairwise model with extra ‘auxiliary ’ variables. We focus on a special case where a much more efficient transformation ..."
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Inference in highorder graphical models has become important in recent years. Several approaches are based, for example, on generalized messagepassing, or on transformation to a pairwise model with extra ‘auxiliary ’ variables. We focus on a special case where a much more efficient transformation is possible. Instead of adding variables, we transform the original problem into a comparatively small instance of submodular vertexcover. These vertexcover instances can then be attacked by existing algorithms (e.g. belief propagation, QPBO), where they often run 4–15 times faster and find better solutions than when applied to the original problem. We evaluate our approach on synthetic data, then we show applications within a fast hierarchical clustering and modelfitting framework.