T.C. Hu. Integer programming and network flows. Addison-Wesley, Reading, Mass., 1969.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....user and network operator and CA is the bound on maximum link capacity. Here ba is the cost of capacity provisioning and rois the unit revenue of the traffic flows fp, p Po w W. In principle our deterministic PCA is a compact arc path form multicommodity flow problem (MFP) in real variables [13]. The given reliability requirement for the network states that each pair w W has a number of node link disjoint paths p P specified by the network operator. As the problem of finding these paths in a given network is computationally exponential, we precompute the required fixed number of paths to ....

Hu, J. (1970). Integer Programming and Network Flows. Addison-Wesley Publishing Company, Inc.

....values from 1 to n. That is, 0 f u n (1) 19 Further since we are interested only in a sequential ordering of the nodes, no two nodes can have the same position, i.e. f u 6= f v for all u 6= v. We represent this relation as an integer linear constraint using the technique proposed by Hu [22]. We use a 0 1 integer variable w u;v and write the condition f u 6= f v as a pair of constraints: f u f v n w u;v (2) f v f u n (1 w u;v ) 3) where n is the number of nodes in the DDG. Intuitively w u;v represents the sign of (f v f u ) and w u;v is 1 if the sign is positive and 0 ....

T. C. Hu. Integer Programming and Network Flows, page 270. Addison-Wesley Pub. Co., 1969.

....column with positive reduced cost. This is of course not feasible in an integer setting because in general after the execution of a simplex pivot the new basic feasible solution is no longer integral. Ways to overcome this difficulty have been proposed by Gomory [Gom63] and Young [You68] see also [Hu69]. The procedure is to generate a Chvatal Gomory cut from one of the legitimate pivot rows in the simplex tableau such that the coefficient of the former pivot element attains the value one in the cut inequality and, secondly, that the cut itself will become a legitimate pivot row. Performing a ....

T. C. Hu, Integer Programming and Network Flows, Addison -- Wesley, Reading, Mass. (1969).

....length of the longer path among the two paths, is less than or equal to X if and only if the instance of ND2PP will have two 13 node disjoint paths from s to d such that the length of the longer path is less than or equal to X. 3 Mathematical Programming Formulation A mathematical programming [14] solution to the optimization version of the EDPP is given next. This formulation seeks to nd a set of k edge disjoint paths from the source to the destination such that the length of the longest path in this set is shortest among all such sets of paths. If only one backup is needed, as is the ....

T. C. Hu, Integer Programming and Network Flows, Addison Wesley Publishing Company, 1970.

....cut and the directed multiway cut problems are at least as large as those for Vertex Cover. As obtaining a ratio better than two for Vertex Cover remains a challenging open problem [23] it appears that Multiway Cut in undirected graphs is easier than its node or directed variations. Finally, Hu [18] proposed Minimum Multicut as an integral dual to maximum multicommodity flow. In this problem, we have to disconnect a list of pairs of terminals. Multiway Cut is a special case, in which the list of pairs forms a clique. Garg et al. 14] give a O(log k) approximation algorithm for Minimum ....

T. C. Hu. Integer Programming and Network Flows. Addison-Wesley, Reading, MA, 1969.

....ows) through the edge (link) e i of the graph G = V; E) under the routing scheme R j . Then the ow number of G = V; E) is fn(G) min 1 j k [ max 1 i m T [i; j] It may be noted that the ow number of a graph can be computed using the techniques known for the multicommodity ow problem [7]. In a sense, it can be viewed as the dual of the multicommodity ow problem. In the multicommodity ow problem, the capacity of the links is known and the objective is to nd the maximum ow that can be attained, subject to the link capacity constraints. In ow number computation, trac demand for ....

T. C. Hu, Integer Programming and Network Flows, Addison Wesley Publishing Company, 1970.

....with positive reduced cost. This is of course not feasible in an integer setting because in general after the execution of a simplex pivot the new basic feasible solution is no longer integral. Ways to overcome this difficulty have been proposed by Gomory [Gom63] and Young [You68] see also [Hu69] The procedure is to generate a Chvatal Gomory cut from one of the legitimate pivot rows in the simplex tableau such that the coefficient of the former pivot element attains the value one in the cut inequality and, secondly, that the cut itself will become a legitimate pivot row. Performing ....

T. C. Hu, Integer programming and network flows, Addison -- Wesley, Reading, Mass., 1969.

....concern in this paper to show how the subproblem of replacing a column can be accomplished e#ectively. For computational results we refer to a companion paper. 1 Introduction Forty years have passed since Ralph Gomory suggested a series of algorithms for tackling linear integer programs; see [Hu69, GN72]. Among these procedures that Gomory proposed are a primal and a dual variant of a so called all integer algorithm. In the course of such a procedure one maintains integrality and primal or dual feasibility, hence the name all integer algorithm. The way to make such an algorithm work is via ....

T. C. Hu, Integer programming and network flows, Addison -- Wesley, Reading, Mass., 1969.

....decomposition R of K. In contrast with the nest Sidney partition, the coarsest Sidney partition R is unique. 3.4 Constructing a Finest Sidney Decomposition We now show how to construct a nest Sidney decomposition, using the GGT algorithm described in Section 3.2. First recall (see, e.g. [6]) that, given a network N = N ; A ; c ) with source s and sink t in N , the collection of sink sets T of all minimum capacity s; t cuts forms a sublattice of 2 N . This sublattice is isomorphic to the sublattice of ideals I N with maximum weight f (I) w(I) p(I) by ....

.... then T is the set of all unlabeled nodes at the end of the procedure (i.e. all nodes not reachable from the source s in the augmenting network associated with the current maximum ow) For T , start from the source s and apply a dual version of Ford Fulkerson s labeling procedure, see [6] for details; then T is the set of all label led nodes at the end of this dual labeling procedure (i.e. all nodes from which one can reach the sink t in the augmenting network) Note that each procedure requires O(m n) operations, where n = jN j = jN j 2 and m = jAj (so the number of arcs ....

T.C. Hu, Integer Programming and Network Flows, Addison{Wesley, Reading, Massachusetts, (1970). 23

....FU assigned to it. That is, if c i and c j represent the colors (or function unit to which they are mapped to) of instructions i and j respectively, then c i 6= c j if both u t;i and u t;j are 1. Such a constraint can be represented in integer programming by adopting the approach given by Hu [30]. We introduce a set of w i;j integer, 0 1 variables, with one such variable for each pair of nodes using the same type of function unit. Roughly speaking these w i;j variables represent the sign of c i Gamma c j . c i Gamma c j u t;i u t;j Gamma 1 2 Gamma N Delta w i;j (26) c j Gamma ....

T. C. Hu, Integer Programming and Network Flows, p. 270. Addison-Wesley Publishing Company, 1969.

....n 3 n 6 n 5 Figure 14: Example of a transformation into the non interfering network flow problem. A similar construction suffices for transforming a problem in Category 2 above to the noninterfering network flow problem. 18 Using standard techniques for computing the max flow in networks [5], the non interfering network flow problem on a network of n nodes and m arcs with unit capacity on arcs, can be solved in time O(nm) 3] Therefore, problems in Category 1 and 2 above can be solved in time O( W 1 W 2 )jT j) 5.2 Switch Block The problem of routing in switch blocks is, in some ....

T.C. Hu. Integer Programming and Network Flows. Addison-Wesley Publishing Company, 1969.

....A is said to be totally unimodular if and only if every sub determinant of A equals 1, 1, or 0. Also, it is known that if A is totally unimodular, so are A T , the transpose matrix of A. We will use the following theorem to prove that our problem can be solved by linear program. Theorem 3.3. 2 [Hu69] A linear program with the constraint Ax b and x 0 always has an integer optimum solution for any arbitrary integer vector b if the matrix A is totally unimodular. We further transform the second optimization problem into the third optimization problem as follows. We let A(u) X(u) r(u) ....

T. C. Hu, Integer Programming and Network Flows, 1969.

.... D ependences dynamiques, Compromis Temp Surface dans un mode le VLSI, Modularit e A Shift Register Based Linear Systolic Array for the General Knapsack Problem 3 1 Introduction The knapsack problem is a classic NP complete, combinatorial optimization problem with a wide range of applications[Hu69, MT90]. Its complexity is pseudo polynomial (it can be solved in time polynomial w.r.t. a parameter which is itself exponential in input size[GJ79] Many time consuming instances of these problems exist[CHR88, Chv80] and so it is a good candidate for efficient parallel implementation on systolic VLSI ....

....where z i is the number of i th objects included in the knapsack. As noted by Teng[Ten90] the performance of parallel algorithms depends on c, m and also the largest and the smallest object weights, wmax and w min (unlike the sequential case when only m and c are relevant) A standard approach[GN72, Hu69] to solving this problem is dynamic programming, which has a well known recurrence equation formulation. In this paper, we address the problem of implementing this on silicon. The main difficulty in obtaining a systolic array for the knapsack recurrence arises from its dynamic dependency, which ....

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T. C. Hu. Integer Programming and Network Flows. Addison-Wesley, 1969.

....computational logic and a pair of xed size FIFOs. A modular solution can be obtained by additional load time control, enabling the processors to pool their bu ers. 1 Introduction The 0 1 knapsack problem is a classic, NP complete, combinatorial optimization problem with many applications [7, 12]. In this paper we concentrate on the dynamic programming approach to this problem [4, 7] since it has more regularity than the dual branch and bound. It is well known that naive dynamic programming performs a lot of redundant computation, which can be avoided by using a sparse representation of ....

....by additional load time control, enabling the processors to pool their bu ers. 1 Introduction The 0 1 knapsack problem is a classic, NP complete, combinatorial optimization problem with many applications [7, 12] In this paper we concentrate on the dynamic programming approach to this problem [4, 7], since it has more regularity than the dual branch and bound. It is well known that naive dynamic programming performs a lot of redundant computation, which can be avoided by using a sparse representation of the data, yielding a signi cant improvement in the average case performance [6] Many ....

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T. C. Hu. { Integer Programming and Network Flows. { Addison-Wesley, 1969.

....for HNF and SNF The computational aspects of Hermite normal form and Smith normal form begun to be more widely investigated about 1950. In 1952 Rosser [4] proposed an algorithm to compute the Hermite normal form using only elementary operations (see Definition 1) D. A. Smith [5] and Hu [8] describe an algorithm which follows a constructive proof of Theorem 3 as is in Newman [13] The algorithm reduces the first row, then proceeds to the first column and if the elements in the first row become to be nonzero the process is repeated. Finally, the first row and column equals zero ....

T. C. Hu, Integer Programming and Network Flows, Addison Wesley, Reading, Mass., 1969.

....as the total capacity of the cut R. This implies that a pruning of minimum loss is a minimum capacity cut from R(G) It is known in the literature that the (unrestricted) min cut problem for an s t planar graph can be reduced to the shortest path problem for its dual graph (see, e.g. Hu69,Law70,Has81] A slight modi cation of the reduction gives us a dual problem for the best pruning (a restricted min cut) problem. Below we show how to construct the dual dag G D from a planar decision dag G that is suitable for our purpose. 7 Assume we have a planar decision dag G = V; E) ....

T. Hu. Integer Programming and Network Flows. Addison-Wesley, 1969.

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T.C. Hu. Integer programming and network flows. Addison-Wesley, Reading, Mass., 1969.

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T.C. Hu. Integer programming and network flows. Addison-Wesley, Reading, Mass., 1969.

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T.C. Hu. Integer programming and network flows. Addison-Wesley, Reading, Mass., 1969.

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T. C. Hu. Integer Programming and Network Flows. Addison-Wesley, 1969.

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T.C. Hu, Integer Programming and Network Flows, p. 270. AddisonWesley, 1969.

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T.C. Hu, Integer Programming and Network Flows, Addison Wesley Publishing, 1969.

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T. C. Hu, Integer Programming and Network Flows,

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T. C. Hu, Integer Programming and Network Flows, Addison Wesley Publishing Company, 1970.

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Hu, T.C., Integer Programming and Network Flows, Reading, MA: Addison-Wesley, 1969.

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