Cutting up a complex object into simpler sub-objects is a fundamental problem in various disciplines. In image processing, images are segmented while in computational geometry, solid polyhedra are decomposed. In recent years, in computer graphics, polygonal meshes are decomposed into sub-meshes. In this paper we propose a novel hierarchical mesh decomposition algorithm. Our algorithm computes a decomposition into the meaningful components of a given mesh, which generally refers to segmentation at regions of deep concavities. The algorithm also avoids over-segmentation and jaggy boundaries between the components. Finally, we demonstrate the utility of the algorithm in control-skeleton extraction.

In the Multiterminal Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, max-flow problem, and can be solved in polynomial time. We show that the problem becomes NP-hard as soon as k = 3, but can be solved in polynomial time for planar graphs for any fixed k. The planar problem is NP-hard, however, if k is not fixed. We also describe a simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2 - 2/k of the optimal cut weight.

In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the Edmonds-Karp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of O(n log n) shortest path problems on networks with n nodes and m arcs and runs in O(n log n (m + n log n)) time. Using a standard transformation, thjis approach yields an O(m log n (m + n log n)) algorithm for the capacitated minimum cost flow problem. This algorithm improves the best previous strongly polynomial time algorithm, due to Z. Galil and E. Tardos, by a factor of n 2 /m. Our algorithm for the capacitated minimum cost flow problem is even more efficient if the number of arcs with finite upper bounds, say n', is much less than m. In this case, the running time of the algorithm is O((m ' + n)log n(m + n log n)).

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. The scaling push-relabel method is an important theoretical development in the area of minimum-cost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve real-life performance of the method. Our implementation works very well over a wide range of problem classes. In our experiments, it was always competitive with the established codes, and usually outperformed these codes by a wide margin. Some heuristics we develop may apply to other network algorithms. Our experimental work on the minimum-cost flow problem motivated theoretical work on related problems. Supported in part by ONR Young Investigator Award N00014-91-J-1855, NSF Presidential Young Investigator Grant CCR-8858097 with matching funds from AT&T and DEC, Stanford University Office of Technology Licensing, and a grant form the Powell Foundation. 1 1. Introduction. Significant theoretical progress has been made recently in the area of minimum-cost flow ...

Abstract. This paper presents a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph’s minimum cut form an extremely small fraction of the graph’s edges. Using this idea, we give a randomized, strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability. The algorithm runs in O(n 2 log 3 n) time, a significant improvement over the previous Õ(mn) time bounds based on maximum flows. It is simple and intuitive and uses no complex data structures. Our algorithm can be parallelized to run in �� � with n 2 processors; this gives the first proof that the minimum cut problem can be solved in ���. The algorithm does more than find a single minimum cut; it finds all of them. With minor modifications, our algorithm solves two other problems of interest. Our algorithm finds all cuts with value within a multiplicative factor of � of the minimum cut’s in expected Õ(n 2 � ) time, or in �� � with n 2 � processors. The problem of finding a minimum multiway cut of a graph into r pieces is solved in expected Õ(n 2(r�1) ) time, or in �� � with n 2(r�1) processors. The “trace ” of the algorithm’s execution on these two problems forms a new compact data structure for representing all small cuts and all multiway cuts in a graph. This data structure can be efficiently transformed into the

When two parallel threads holding no locks in common access the same memory location and at least one of the threads modifies the location, a “data race ” occurs, which is usually a bug. This paper describes the algorithms and strategies used by a debugging tool, called the Nondeterminator-2, which checks for data races in programs coded in the Cilk multithreaded language. Like its predecessor, the Nondeterminator, which checks for simple “determinacy” races, the Nondeterminator-2 is a debugging tool, not a verifier, since it checks for data races only in the computation generated by a serial execution of the program on a given input. We give an algorithm, ALL-SETS, that determines whether the computation generated by a serial execution of a Cilk program on a given input contains a race. For a program that runs serially in time T, accesses V shared memory locations, uses a total of n locks, and holds at most k n locks simultaneously, ALL-SETS runs in O(nkT α(V;V))time and O(nk α(V;V)) V)space, where α is Tarjan’s functional inverse of Ackermann’s function. Since ALL-SETS may be too inefficient in the worst case, we propose a much more efficient algorithm which can be used to detect races in programs that obey the “umbrella ” locking discipline, a programming methodology that is more flexible than similar disciplines proposed in the literature. We present an algorithm, BRELLY, which detects violations of the umbrella discipline in O(kT time Keywords using O(kV)space. We also prove that any “abelian ” Cilk program, one whose critical sections commute, produces a determinate final state if it is deadlock free and if it generates any computation which is datarace free. Thus, the Nondeterminator-2’s two algorithms can verify the determinacy of a deadlock-free abelian program running on a given input.

Combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics. This paper focusses on possibly the simplest application of graph-cuts: segmentation of objects in image data. Despite its simplicity, this application epitomizes the best features of combinatorial graph cuts methods in vision: global optima, practical efficiency, numerical robustness, ability to fuse a wide range of visual cues and constraints, unrestricted topological properties of segments, and applicability to N-D problems. Graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes, geodesic active contours, and level-sets. The segmentation energies optimized by graph cuts combine boundary regularization with region-based properties in the same fashion as Mumford-Shah style functionals. We present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s/t graph cuts. After the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in Boykov and Jolly (2001), this idea was widely studied in computer vision and graphics communities. We provide links to a large number of known extensions based on iterative parameter re-estimation and learning, multi-scale or hierarchical approaches, narrow bands, and other techniques for demanding photo, video, and medical applications.

A large body of work has been devoted to identifying community structure in networks. A community is often though of as a set of nodes that has more connections between its members than to the remainder of the network. In this paper, we characterize as a function of size the statistical and structural properties of such sets of nodes. We define the network community profile plot, which characterizes the “best ” possible community—according to the conductance measure—over a wide range of size scales, and we study over 70 large sparse real-world networks taken from a wide range of application domains. Our results suggest a significantly more refined picture of community structure in large real-world networks than has been appreciated previously. Our most striking finding is that in nearly every network dataset we examined, we observe tight but almost trivial communities at very small scales, and at larger size scales, the best possible communities gradually “blend in ” with the rest of the network and thus become less “community-like.” This behavior is not explained, even at a qualitative level, by any of the commonly-used network generation models. Moreover, this behavior is exactly the opposite of what one would expect based on experience with and intuition from expander graphs, from graphs that are well-embeddable in a low-dimensional structure, and from small social networks that have served as testbeds of community detection algorithms. We have found, however, that a generative model, in which new edges are added via an iterative “forest fire” burning process, is able to produce graphs exhibiting a network community structure similar to our observations.

Authentication using a path of trusted intermediaries, each able to authenticate the next in the path, is a well-known technique for authenticating entities in a large-scale system. Recent work has extended this technique to include multiple paths in an effort to bolster authentication, but the success of this approach may be unclear in the face of intersecting paths, ambiguities in the meaning of certificates, and interdependencies in the use of different keys. Thus, several authors have proposed metrics to evaluate the confidence afforded by a set of paths. In this paper we develop a set of guiding principles for the design of such metrics. We motivate our principles by showing how previous approaches failed with respect to these priniciples and what the consequences to authentication might be. We then propose a new metric that appears to meet our principles, and so to be a satisfactory metric of authentication.