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The Complexity of Multiterminal Cuts
 SIAM Journal on Computing
, 1994
"... In the Multiterminal Cut problem we are given an edgeweighted 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, maxflow problem, and ..."
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Cited by 190 (0 self)
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In the Multiterminal Cut problem we are given an edgeweighted 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, maxflow problem, and can be solved in polynomial time. We show that the problem becomes NPhard as soon as k = 3, but can be solved in polynomial time for planar graphs for any fixed k. The planar problem is NPhard, 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.
Finding kcuts within Twice the Optimal
, 1995
"... Two simple approximation algorithms for the minimum kcut problem are presented. Each algorithm finds a kcut having weight within a factor of (2 \Gamma 2=k) of the optimal. One of our algorithms is particularly efficient  it requires a total of only n \Gamma 1 maximum flow computations for find ..."
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Cited by 48 (2 self)
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Two simple approximation algorithms for the minimum kcut problem are presented. Each algorithm finds a kcut having weight within a factor of (2 \Gamma 2=k) of the optimal. One of our algorithms is particularly efficient  it requires a total of only n \Gamma 1 maximum flow computations for finding a set of nearoptimal kcuts, one for each value of k between 2 and n. i 1 Introduction The minimum kcut problem is as follows: given an undirected graph G = (V; E) with nonnegative edge weights and a positive integer k, find a set S ` E of minimum weight whose removal leaves k connected components. This problem is of considerable practical significance, especially in the area of VLSI design. Solving this problem exactly is NPhard [GH], but no efficient approximation algorithms were known for it. In this paper we give two simple algorithms for finding kcuts. We prove a performance guarantee of (2 \Gamma 2=k) for each algorithm; however, neither algorithm dominates the other on a...
Performance analysis and best implementations of old and new algorithms for the OpenPit Mining Problem
 Operations Research
, 1998
"... The openpit mining problem is to determine the contours of a mine, based on economic data and engineering feasibility requirements in order to yield maximumpossible net income. This practical problem needs to be solved for very large data sets. In practice, moreover, it is necessary to test mult ..."
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Cited by 15 (1 self)
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The openpit mining problem is to determine the contours of a mine, based on economic data and engineering feasibility requirements in order to yield maximumpossible net income. This practical problem needs to be solved for very large data sets. In practice, moreover, it is necessary to test multiple scenarios taking into account a variety of realizations of geological predictions and forecasts of ore value. The industry is experiencing computational difficulties in solving the problem. Yet, the problem is known to be equivalent to the minimum cut or maximum flow problem. For the maximum flow problem there are a number of very efficient algorithms that have been developed over the last decade. On the other hand, the algorithm that is most commonly used by the mining industry has been devised by Lerchs and Grossmann (LG) [LG64]. This algorithm is used in most commercial software packages for openpit mining. This paper describes a detailed study of the LG algorithm as compare...
Probabilistic Analysis of Network Flow Algorithms
 Mathematics of Operations Research
, 1995
"... This paper is concerned with the design and probabilistic analysis of algorithms for the maximumflow problem and capacitated transportation problems. These algorithms run in linear time and, under certain assumptions about the probability distribution of edge capacities, obtain an optimal solution w ..."
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Cited by 7 (1 self)
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This paper is concerned with the design and probabilistic analysis of algorithms for the maximumflow problem and capacitated transportation problems. These algorithms run in linear time and, under certain assumptions about the probability distribution of edge capacities, obtain an optimal solution with high probability. The design of our algorithms is based on the following general method, which we call the mimicking method, for solving problems in which some of the input data is deterministic and some is random with a known distribution: 1. Replace each random variable in the problem by its expectation; this gives a deterministic problem instance that has a special form, making it particularly easy to solve; 2. Solve the resulting deterministic problem instance; 3. Taking into account the actual values of the random variables, mimic the solution of the deterministic instance to obtain a nearoptimal solution to the original problem; 4. Finetune this suboptimal solution to obtain an o...
RREACT: A Distributed Protocol for Rapid Restoration of Active Communication Trunks
, 1993
"... Commercial telecommunications networks have tight realtime requirements for restoration after a failure. The problem of finding the available restoration paths and reassigning the interrupted traffic within such tight realtime requirements places difficult demands on the restoration protocol emplo ..."
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Cited by 4 (2 self)
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Commercial telecommunications networks have tight realtime requirements for restoration after a failure. The problem of finding the available restoration paths and reassigning the interrupted traffic within such tight realtime requirements places difficult demands on the restoration protocol employed. This paper reviews several distributed network restoration protocols and presents a new distributed protocol called RREACT, for performing this function with a distributed algorithm which uses no prior network status or topography knowledge and which supports multiple simultaneous link restorations. Simulation results show that this protocol significantly outperforms other existing algorithms based on the SenderChooser approach, usually completing the total restoration in well under one second. In addition, enhancements to the basic algorithm are described which help to ensure nearoptimal use of network spare channel resources and address such restoration situations where a complete r...
Physical Models And Efficient Algorithms For OverTheCell Routing In Standard Cell Design
 IEEE Trans. on CAD
, 1993
"... When an overthecell routing layer is available for standard cell layout, efficient utilization of that routing space over the cells can significantly reduce layout area. In this paper, we present three physical models to utilize the area over the cells for routing in standard cell designs. We also ..."
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When an overthecell routing layer is available for standard cell layout, efficient utilization of that routing space over the cells can significantly reduce layout area. In this paper, we present three physical models to utilize the area over the cells for routing in standard cell designs. We also present efficient algorithms to choose and to route a planar subset of nets over the cells so that the resulting channel density is reduced as much as possible. For each of the physical models, we show how to arrange intercell routing, overthecell routing and power/ground busses to achieve valid routing solutions. Each algorithm exploits the particular arrangement in the corresponding physical model and produces provably good results in polynomial time. We tested our algorithms on two industrial standard cell designs. In these tests, this method reduces total channel density as much as 21%. 1. Introduction Standard cells are widely used in the design of VLSI circuits. After the cells a...
Minimum Ratio Canceling is Oracle Polynomial for Linear Programming, but Not Strongly Polynomial, Even for Networks
, 1999
"... This paper shows that the minimum ratio canceling algorithm of Wallacher (1989) (and a faster relaxed version) can be generalized to an algorithm for general linear programs with geometric convergence. This implies that when we have a negative cycle oracle, this algorithm will compute an optimal sol ..."
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This paper shows that the minimum ratio canceling algorithm of Wallacher (1989) (and a faster relaxed version) can be generalized to an algorithm for general linear programs with geometric convergence. This implies that when we have a negative cycle oracle, this algorithm will compute an optimal solution in (weakly) polynomial time. We then specialize the algorithm to linear programming on unimodular linear spaces, and to the minimum cost flow and (dual) tension problems. We construct instances proving that even in the network special cases the algorithm is not strongly polynomial. Keywords: negative cycle canceling algorithm, minimum ratio cycle, linear programming problem, unimodular linear space, minimum cost flow, minimum cost tension. 1
Efficient Procedures for Minimizing the Standby Power in Dual V_T CMOS Circuits
"... In this paper we present efficient procedures for delay constrained minimization of the power due to leakage in CMOS digital circuits for a dual threshold voltage (V T ) technology. The availability of two or more threshold voltages on the same chip provides a new opportunity for circuit designers t ..."
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In this paper we present efficient procedures for delay constrained minimization of the power due to leakage in CMOS digital circuits for a dual threshold voltage (V T ) technology. The availability of two or more threshold voltages on the same chip provides a new opportunity for circuit designers to make tradeoffs between power and delay. We present two efficient procedures that take as input a gate level netlist and assign the proper threshold voltage to each transistor so that the leakage power is minimized but without violating the delay constraints. Experimental results on the MCNC91 benchmark circuits show that up to one order of magnitude power reduction can be achieved without any delay increase when compared to a circuit where all transistors are low V T devices. 1 Introduction The advent of deep submicron devices has given rise to new challenges as well as new opportunities for the optimal design of CMOS circuits. Many of the parameters of a MOSFET that are traditionally co...
A WellBehaved Extension of the Vertex Covering Problem
"... The paper shows that several wellknown results on properties of optimal solutions of the minimum weight vertex covering problem (Balinski [1], Balinski and Spielberg [2], Nemhauser and Trotter [8], Hammer et al.[7], Bourjolly et al.[3]) remain true for an extension of it. 1 Introduction Let G = (V ..."
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The paper shows that several wellknown results on properties of optimal solutions of the minimum weight vertex covering problem (Balinski [1], Balinski and Spielberg [2], Nemhauser and Trotter [8], Hammer et al.[7], Bourjolly et al.[3]) remain true for an extension of it. 1 Introduction Let G = (V; E) be a undirected graph with vertex set V and edge set E. A subset X ` V is called a vertex covering if every edge of G has at least one endpoint in X. The minimum weight vertex covering problem (VCP) is, given a graph G with positive vertex weights c i (i 2 V ), to find a vertex covering X with the minimum weight P i2X c i . Clearly, a set X ` V is a vertex covering if and only if its complement V n X consists of pairwise nonadjacent vertices, i.e., is stable. So finding a minimum weight vertex covering is equivalent to finding a maximum weight stable set. Both problems are classic in discrete optimization and have been extensively investigated for recent decades. Despite NPhard...