Minimum-Weight Link-Disjoint Node-“Somewhat Disjoint” Paths

Network survivability has drawn certain interest in network optimization. However, the demand for full protection of a network is usually too restrictive. To overcome the limitation of geographical environments and to save network resources, we turn to establish backup networks allowing a few common nodes. It comes out the problem of finding k link-disjoint paths between a given pair of source and sink in a network such that the number of common nodes shared by at least two paths is bounded by a constant and the total link weight of all paths is minimized under the above constraints. For the case k = 2, where we have only one backup path, several fast algorithms have been developed in the literature. For the case k > 2, little results are known. In this paper, we first establish the NP-hardness of the problem with general k. Motivated by the situation that each node in a network may have a capability of multicasting, we also study a restricted version with one more requirement that each node can be shared by at most two paths. For the restricted version, we build an ILP model and design a fast algorithm by using the techniques of augmenting paths and splitting nodes. Furthermore, experimental results on synthetic and real networks show that our algorithm is effective in practice.

Download Full-text

Disjoint paths of bounded length in large generalized cycles

Discrete Mathematics ◽

10.1016/s0012-365x(98)00240-4 ◽

1999 ◽

Vol 197-198 (1-3) ◽

pp. 285-298 ◽

Cited By ~ 1

Author(s):

D Ferrero

Keyword(s):

Disjoint Paths

Download Full-text

Further Studies on the Mechanisms for the Antithrombotic Effects of Sulfated Polysaccharides in Rabbits

Thrombosis and Haemostasis ◽

10.1055/s-0038-1647027 ◽

1988 ◽

Vol 60 (02) ◽

pp. 188-192 ◽

Cited By ~ 15

Author(s):

F A Ofosu ◽

F Fernandez ◽

N Anvari ◽

C Caranobe ◽

F Dol ◽

...

Keyword(s):

Antithrombin Iii ◽

Ex Vivo ◽

Thrombus Formation ◽

Minimum Weight ◽

Sulfated Polysaccharides ◽

Pentosan Polysulfate ◽

Heparin Cofactor Ii ◽

Thrombin Inhibition ◽

The Relationship ◽

Prothrombin Activation

SummaryA recent study (Fernandez et al., Thromb. Haemostas. 1987; 57: 286-93) demonstrated that when rabbits were injected with the minimum weight of a variety of glycosaminoglycans required to inhibit tissue factor-induced thrombus formation by —80%, exogenous thrombin was inactivated —twice as fast in the post-treatment plasmas as the pre-treatment plasmas. In this study, we investigated the relationship between inhibition of thrombus formation and the extent of thrombin inhibition ex vivo. We also investigated the relationship between inhibition of thrombus formation and inhibition of prothrombin activation ex vivo. Four sulfated polysaccharides (SPS) which influence coagulation in a variety of ways were used in this study. Unfractionated heparin and the fraction of heparin with high affinity to antithrombin III potentiate the antiproteinase activity of antithrombin III. Pentosan polysulfate potentiates the activity of heparin cofactor II. At less than 10 pg/ml of plasma, all three SPS also inhibit intrinsic prothrombin activation. The fourth agent, dermatan sulfate, potentiates the activity of heparin cofactor II but fails to inhibit intrinsic prothrombin activation even at concentrations which exceed 60 pg/ml of plasma. Inhibition of thrombus formation by each sulfated polysaccharides was linearly related to the extent of thrombin inhibition achieved ex vivo. These observations confirm the utility of catalysis of thrombin inhibition as an index for assessing antithrombotic potential of glycosaminoglycans and other sulfated polysaccharides in rabbits. With the exception of pentosan polysulfate, there was no clear relationship between inhibition of thrombus formation and inhibition of prothrombin activation ex vivo.

Download Full-text

CARTECH Ti-3Al-8V-6Cr-4Mo-4Zr (BETA C)

Alloy Digest ◽

10.31399/asm.ad.ti0172 ◽

2020 ◽

Vol 69 (11) ◽

Keyword(s):

Corrosion Resistance ◽

Minimum Weight ◽

High Strength ◽

Heat Treating ◽

Beta Alloy ◽

Heat Treated ◽

Technology Corporation ◽

Carpenter Technology Corporation ◽

Metastable Beta ◽

Good Workability

Abstract CarTech Ti-3Al-8V-6Cr-4Mo-4Zr, also known as Ti-3-8-6-4-4 and Beta C, is a metastable beta alloy used in the solution heat treated or solution heat treated and aged condition. It is appropriate for applications where very high strength, minimum weight, and corrosion resistance are important. Ti-3Al-8V-6Cr-4Mo-4Zr has gained in popularity among beta alloys because it is easier to melt and process, exhibiting low segregation, good workability, and good heat-treating properties. This datasheet provides information on composition, physical properties, elasticity, and tensile properties. It also includes information on corrosion resistance as well as forming, heat treating, machining, and joining. Filing Code: Ti-172. Producer or source: Carpenter Technology Corporation.

Download Full-text

The identification of minimum-weight sound packages

Noise Control Engineering Journal ◽

10.3397/1/376644 ◽

2018 ◽

Vol 66 (6) ◽

pp. 523-540 ◽

Cited By ~ 1

Author(s):

Hyunjun Shin ◽

J. Stuart Bolton

Keyword(s):

Minimum Weight

Download Full-text

Quadruple Roman Domination in Trees

Symmetry ◽

10.3390/sym13081318 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1318

Author(s):

Zheng Kou ◽

Saeed Kosari ◽

Guoliang Hao ◽

Jafar Amjadi ◽

Nesa Khalili

Keyword(s):

Open Neighborhood ◽

Minimum Weight ◽

Domination Number ◽

Theoretical Computer Science ◽

Upper And Lower Bounds ◽

Discrete Mathematics ◽

Roman Domination ◽

Roman Domination Number ◽

Vertex Set ◽

Roman Dominating Function

This paper is devoted to the study of the quadruple Roman domination in trees, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. For any positive integer k, a [k]-Roman dominating function ([k]-RDF) of a simple graph G is a function from the vertex set V of G to the set {0,1,2,…,k+1} if for any vertex u∈V with f(u)<k, ∑x∈N(u)∪{u}f(x)≥|{x∈N(u):f(x)≥1}|+k, where N(u) is the open neighborhood of u. The weight of a [k]-RDF is the value Σv∈Vf(v). The minimum weight of a [k]-RDF is called the [k]-Roman domination number γ[kR](G) of G. In this paper, we establish sharp upper and lower bounds on γ[4R](T) for nontrivial trees T and characterize extremal trees.

Download Full-text