Abstract—In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper, we give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of binary variables. However, our work generalizes many previous constructions and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration, and scene reconstruction. We give a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables. We also provide a general-purpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. Researchers who are considering the use of graph cuts to optimize a particular energy function can use our results to determine if this is possible and then follow our construction to create the appropriate graph. A software implementation is freely available.

Since 1984, the Condor project has enabled ordinary users to do extraordinary computing. Today, the project continues to explore the social and technical problems of cooperative computing on scales ranging from the desktop to the world-wide computational grid. In this chapter, we provide the history and philosophy of the Condor project and describe how it has interacted with other projects and evolved along with the field of distributed computing. We outline the core components of the Condor system and describe how the technology of computing must correspond to social structures. Throughout, we reflect on the lessons of experience and chart the course traveled by research ideas as they grow into production systems.

This paper surveys the design of embedded computer systems, which use software running on programmable computers to im-plement system functions. Creating an embedded computer system which meets its performance, cost, and design time goals is a hardware-software co-design problewhe design of the hard-ware and software components influence each other. This paper emphasizes a historical approach to show the relationships be-tween well-understood design problems and the as-yet unsolved problems in co-design. We describe the relationship between hard-ware and sofhvare architecture in the early stages of embedded system design. We describe analysis techniques for hardware and software relevant to the architectural choices required for hard-ware-software co-design. We also describe design and synthesis techniques for co-design and related problems.

Since 1984, the Condor project has helped ordinary users to do extraordinary computing. Today, the project continues to explore the social and technical problems of cooperative computing on scales ranging from the desktop to the world-wide computational grid. In this chapter, we provide the history and philosophy of the Condor project and describe how it has interacted with other projects and evolved along with the field of distributed computing. We outline the core components of the Condor system and describe how the technology of computing must reflect the sociology of communities. Throughout, we reflect on the lessons of experience and chart the course travelled by research ideas as they grow into production systems.

Devices]: Modes of Computation---Parallelism and concurrency General Terms: Algorithms, Design, Performance, Theory Additional Key Words and Phrases: Automatic parallelization, DAG, multiprocessors, parallel processing, software tools, static scheduling, task graphs This research was supported by the Hong Kong Research Grants Council under contract numbers HKUST 734/96E, HKUST 6076/97E, and HKU 7124/99E. Authors' addresses: Y.-K. Kwok, Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong; email: ykwok@eee.hku.hk; I. Ahmad, Department of Computer Science, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong. Permission to make digital / hard copy of part or all of this work for personal or classroom use is granted without fee provided that the copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication, and its date appear, and notice is given that copying is by permission of the ACM, Inc. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and / or a fee. 2000 ACM 0360-0300/99/1200--0406 $5.00 ACM Computing Surveys, Vol. 31, No. 4, December 1999 1.

Abstract. One of the most exciting advances in early vision has been the development of efficient energy minimization algorithms. Many early vision tasks require labeling each pixel with some quantity such as depth or texture. While many such problems can be elegantly expressed in the language of Markov Random Fields (MRF’s), the resulting energy minimization problems were widely viewed as intractable. Recently, algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: for example, such methods form the basis for almost all the top-performing stereo methods. Unfortunately, most papers define their own energy function, which is minimized with a specific algorithm of their choice. As a result, the tradeoffs among different energy minimization algorithms are not well understood. In this paper we describe a set of energy minimization benchmarks, which we use to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods—graph cuts, LBP, and tree-reweighted message passing—as well as the well-known older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching and interactive segmentation. We also provide a general-purpose software interface that allows vision researchers to easily switch between optimization methods with minimal overhead. We expect that the availability of our benchmarks and interface will make it significantly easier for vision researchers to adopt the best method for their specific problems. Benchmarks, code, results and images are available at

One goal of locally distributed systems is to facilitate resource sharing. Most current locally distributed systems, however, share primarily data, data storage devices, and output devices; there is little sharing of computational resourees. Load shoring is the process of sharing computational resources by transparently distributing the system workload. System performance can be improved by transferring work from nodes that are heavily loaded to nodes that are lightly loaded. Load sharing policies may be either static or adaptive. Static policies use only information about the average behavior of the system; transfer decisions are independent of the actual current system state. Static policies may be either deterministic (e.g., “transfer all compilations originating at node A to server B”) or probabilistic (e.g., “transfer half of the compilations originating at node A to server B, and process the other half locally”). Numerous

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.

It is now more than a quarter of a century since researchers started publishing papers on mapping strategies for distributing computation across the computation resource of multiprocessor systems. There exists a large body of literature on the subject, but there is no commonly-accepted framework whereby results in the field can be compared. Nor is it always easy to assess the relevance of a new result to a particular problem. Furthermore, changes in parallel computing technology have made some of the earlier work of less relevance to current multiprocessor systems. Versions of the mapping problem are classified, and research in the field is considered in terms of its relevance to the problem of programming currently available hardware in the form of a distributed memory multiple instruction stream multiple data stream computer: a multicomputer.

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadratic assignment problem, and discusses the relationship between the QAP and other well known combinatorial optimization problems, e.g. the traveling salesman problem, the graph partitioning problem, etc. The paper will appear in the Handbook of Combinatorial Optimization to be published by Kluwer Academic Publishers, P. Pardalos and D.-Z. Du, eds.