A combinatorial arc tolerance analysis for network flow problems

For the separable convex cost flow problem, we consider the problem of determining tolerance set for each arc cost function. For a given optimal flow x, a valid perturbation of cij(x) is a convex function that can be substituted for cij(x) in the total cost function without violating the optimality of x. Tolerance set for an arc(i,j) is the collection of all valid perturbations of cij(x). We characterize the tolerance set for each arc(i,j) in terms of nonsingleton shortest distances between nodes i and j. We also give an efficient algorithm to compute the nonsingleton shortest distances between all pairs of nodes in O(n3) time where n denotes the number of nodes in the given graph

Synthesis and photophysical studies of non-covalently linked porphyrin dyads and triads

Non-covalent porphyrin dyads and triads containing N3S porphyrin and RuN4 porphyrin subunits were synthesized by treating meso-pyridyl-21-thiaporphyrin with RuTPP(CO)(EtOH) in toluene at refluxing temperature. The dyads and triads were characterized by various spectroscopic techniques and the properties were compared with the reported dyad containing N-4 and RuN4 porphyrin subunits. The H-1 NMR study of dyads and triads indicated that the inner NH, beta-heterocycle and meso-pyridyl protons of the 21-thiaporphyrin unit experienced large upfield shifts as compared to their corresponding monomeric meso-pyridyl-21-thiaporphyrins due to the ring current effect of RuTPP(CO) subunit. The singlet state photophysical properties of N3S porphyrin subunit in dyads and triads showed 50-80% quenching of fluorescence as observed previously for N-4-RuN4 dyad due to heavy ruthenium ion(s). Copyright (c) 2007 Society of Porphyrins & Phthalocyanines

A COMBINATORIAL ARC TOLERANCE ANALYSIS FOR NETWORK FLOW PROBLEMS

For the separable convex cost flow problem, we consider the problem of determining tolerance set for each arc cost function. For a given optimal flow x, avalidperturbation of cij(x) is a convex function that can be substituted for cij(x) in the total cost function without violating the optimality of x. Tolerance set for an arc(i, j) is the collection of all valid perturbations of cij(x). We characterize the tolerance set for each arc(i, j)intermsof nonsingleton shortest distances between nodes i and j.Wealsogiveanefficient algorithm to compute the nonsingleton shortest distances between all pairs of nodes in O(n 3)time where n denotes the number of nodes in the given graph. 1

Inverse spanning tree problems : formulations and algorithms

Cover title

New Polynomial-Time Cycle-Canceling Algorithms for Minimum Cost Flows

The cycle-canceling algorithm is one of the earliest algorithms to solve the minimum cost flow problem. This algorithm maintains a feasible solution x in the network G and proceeds by augmenting flows along negative cost directed cycles in the residual network G(x) and thereby canceling them. For the minimum cost flow problem with integral data, the generic version of the cycle-canceling algorithm runs in pseudo-polynomial time, but several polynomial-time specific implementations can be obtained by specifying the choices of cycles to be canceled. In this paper, we describe a new cycle-canceling algorithm that solves the minimum cost flow problem in polynomial time. Our algorithm is a scaling algorithm and proceeds by augmenting flows along negative cycles with "sufficiently large" residual capacity. Further, it identifies such a cycle by solving a shortest path problem with nonnegative arc lengths. For a network with n nodes and m arcs, our cycle-canceling algorithm performs O(m log(nU)) augmentations and runs in O(m(m + n log n) log(nU)) time, where U is an upper bound on the node supples/demands and finite arc capacities. We next describe a variant of algorithm that solves the minimum cost flow problem in strongly polynomial time; the running time of this variant is O(m(m+n log n) min{log (nU), m log n})

Tungsten Matrix Composite Reinforced with CoCrFeMnNi High-Entropy Alloy: Impact of Processing Routes on Microstructure and Mechanical Properties

Tungsten heavy alloy composite was developed by using novel CoCrFeMnNi high-entropy alloy as the binder/reinforcement phase. Elemental tungsten (W) powder and mechanically alloyed CoCrFeMnNi high-entropy alloy were mixed gently in high energy ball mill and consolidated using different sintering process with varying heating rate (in trend of conventional sintering < microwave sintering < spark plasma sintering). Mechanically alloyed CoCrFeMnNi high-entropy alloy have shown a predominant face-centered cubic (fcc) phase with minor Cr-rich σ-phase. Consolidated tungsten heavy high-entropy alloys (WHHEA) composites reveal the presence of Cr–Mn-rich oxide phase in addition to W-grains and high-entropy alloys (HEA) phase. An increase in heating rate restricts the tungsten grain growth with reduces the volume fraction of the Cr–Mn-rich phase. Finally, spark plasma sintering with a higher heating rate and shorter sintering time has revealed higher compressive strength (~2041 MPa) than the other two competitors (microwave sintering: ~1962 MPa and conventional sintering: ~1758 MPa), which may be attributed to finer W-grains and reduced fraction of Cr–Mn rich oxide phase

New polynomial-time cycle-canceling algorithms for minimum cost flows

HD28 .M414 no.3914-96,