Theoretical Computer Science, ISSN 0304-3975, 08/2009, Volume 410, Issue 36, pp. 3428 - 3435

Given an instance of the Steiner tree problem together with an optimal solution, we consider the scenario where this instance is modified locally by adding one...

Reoptimization | Steiner tree | Approximation algorithms | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Algorithms | Steiner trees | Data- och informationsvetenskap | approximation | Naturvetenskap | Computer Sciences | Datavetenskap (datalogi) | Natural Sciences | Computer and Information Sciences | reoptimization

Reoptimization | Steiner tree | Approximation algorithms | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Algorithms | Steiner trees | Data- och informationsvetenskap | approximation | Naturvetenskap | Computer Sciences | Datavetenskap (datalogi) | Natural Sciences | Computer and Information Sciences | reoptimization

Journal Article

Discrete Mathematics, ISSN 0012-365X, 05/2017, Volume 340, Issue 5, pp. 1042 - 1045

The existence of Large sets of Kirkman Triple Systems (LKTS) is an old problem in combinatorics. Known results are very limited, and a lot of them are based on...

Large set | Steiner triple system | Kirkman triple system

Large set | Steiner triple system | Kirkman triple system

Journal Article

Wireless Communications and Mobile Computing, ISSN 1530-8669, 12/2005, Volume 5, Issue 8, pp. 927 - 932

Since no fixed infrastructure and no centralized management present in wireless networks, a connected dominating set (CDS) of the graph representing the...

Greedy algorithm | Wireless network | Maximal independent set | Connected dominating set | APPROXIMATION | STEINER POINTS | connected dominating set | maximal independent set | UNIT DISK GRAPHS | COMPUTER SCIENCE, INFORMATION SYSTEMS | TELECOMMUNICATIONS | wireless network | greedy algorithm | MINIMUM NUMBER | HEURISTICS | ENGINEERING, ELECTRICAL & ELECTRONIC

Greedy algorithm | Wireless network | Maximal independent set | Connected dominating set | APPROXIMATION | STEINER POINTS | connected dominating set | maximal independent set | UNIT DISK GRAPHS | COMPUTER SCIENCE, INFORMATION SYSTEMS | TELECOMMUNICATIONS | wireless network | greedy algorithm | MINIMUM NUMBER | HEURISTICS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2015, Volume 47, Issue 2, pp. 1489 - 1529

In this paper we provide an approximation a la Ambrosio-Tortorelli of some classical minimization problems involving the length of one-dimensional sets. The...

Networks | Gamma-convergence | Fast marching | Steiner | Minkowsky content | TRAFFIC CONGESTION | MATHEMATICS, APPLIED | AVERAGE-DISTANCE PROBLEM | gamma-convergence | DIRICHLET REGIONS | networks | OPTIMAL TRANSPORTATION | MINIMIZERS | EQUILIBRIA | IRRIGATION PROBLEM | OPTIMIZATION | PARTITIONS | fast marching | Lower bounds | Approximation | Mathematical analysis | Proving | Minimization | Optimization | Convergence | Mathematics | General Mathematics

Networks | Gamma-convergence | Fast marching | Steiner | Minkowsky content | TRAFFIC CONGESTION | MATHEMATICS, APPLIED | AVERAGE-DISTANCE PROBLEM | gamma-convergence | DIRICHLET REGIONS | networks | OPTIMAL TRANSPORTATION | MINIMIZERS | EQUILIBRIA | IRRIGATION PROBLEM | OPTIMIZATION | PARTITIONS | fast marching | Lower bounds | Approximation | Mathematical analysis | Proving | Minimization | Optimization | Convergence | Mathematics | General Mathematics

Journal Article

Optical Switching and Networking, ISSN 1573-4277, 11/2019, Volume 34, pp. 35 - 46

This paper introduces the Multi-Server Multicast (MSM) approach for Content Delivery Networks (CDNs) delivering services offered by a set of Data Centers...

Degree-constrained steiner problem | Data centers elastic optical networks | Physical layer impairments | Light-hierarchy | ILP | Multicast session planning | COMPUTER SCIENCE, INFORMATION SYSTEMS | OPTICS | TELECOMMUNICATIONS | Fiber optic networks | Network switches | Complexitat computacional | Computational complexity | Optical communications | Enginyeria de la telecomunicació | Comunicacions òptiques | Telecomunicació òptica | Routing (Computer network management) | Encaminadors (Xarxes d'ordinadors) | Àrees temàtiques de la UPC | Mathematics | Combinatorics | Networking and Internet Architecture | Computer Science | Operations Research

Degree-constrained steiner problem | Data centers elastic optical networks | Physical layer impairments | Light-hierarchy | ILP | Multicast session planning | COMPUTER SCIENCE, INFORMATION SYSTEMS | OPTICS | TELECOMMUNICATIONS | Fiber optic networks | Network switches | Complexitat computacional | Computational complexity | Optical communications | Enginyeria de la telecomunicació | Comunicacions òptiques | Telecomunicació òptica | Routing (Computer network management) | Encaminadors (Xarxes d'ordinadors) | Àrees temàtiques de la UPC | Mathematics | Combinatorics | Networking and Internet Architecture | Computer Science | Operations Research

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 2/2016, Volume 31, Issue 2, pp. 713 - 724

A $$k$$ k -connected (resp. $$k$$ k -edge connected) dominating set $$D$$ D of a connected graph $$G$$ G is a subset of $$V(G)$$ V ( G ) such that $$G[D]$$ G [...

Connected dominating set | Dominating set | Convex and Discrete Geometry | Independent set | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Optimization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CHORDAL GRAPHS | ALGORITHMS | STEINER TREES

Connected dominating set | Dominating set | Convex and Discrete Geometry | Independent set | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Optimization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CHORDAL GRAPHS | ALGORITHMS | STEINER TREES

Journal Article

Journal of Combinatorial Designs, ISSN 1063-8539, 08/2015, Volume 23, Issue 8, pp. 321 - 327

A cross‐free set of size m in a Steiner triple system (V,B) is three pairwise disjoint m‐element subsets X1,X2,X3⊂V such that no B∈B intersects all the three...

Steiner triple systems | edge coloring of hypergraphs | MATHEMATICS | Mathematics - Combinatorics

Steiner triple systems | edge coloring of hypergraphs | MATHEMATICS | Mathematics - Combinatorics

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 10/2017, Volume 34, Issue 3, pp. 956 - 963

This paper studies the minimum weight partial connected set cover problem (PCSC). Given an element set U, a collection $${\mathcal {S}}$$ S of subsets of U, a...

Partial connected set cover | Convex and Discrete Geometry | Operations Research/Decision Theory | Budgeted connected set cover | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Approximation algorithm | Optimization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STEINER TREE | Algorithms

Partial connected set cover | Convex and Discrete Geometry | Operations Research/Decision Theory | Budgeted connected set cover | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Approximation algorithm | Optimization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STEINER TREE | Algorithms

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 4/2018, Volume 41, Issue 2, pp. 627 - 636

In this paper we prove some bounds for Steiner distance in Cartesian product. We investigate properties of connected subgraphs that are not Steiner convex....

05C76 | 05C12 | Grid | Mathematics, general | Mathematics | Steiner convexity | Applications of Mathematics | Cartesian product | 05C38 | MATHEMATICS | DISTANCE | TREES | INTERVALS | GRAPHS | Convexity | Cartesian coordinates

05C76 | 05C12 | Grid | Mathematics, general | Mathematics | Steiner convexity | Applications of Mathematics | Cartesian product | 05C38 | MATHEMATICS | DISTANCE | TREES | INTERVALS | GRAPHS | Convexity | Cartesian coordinates

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2018, Volume 50, Issue 6, pp. 6307 - 6332

In this paper we consider variational problems involving 1-dimensional connected sets in the Euclidean plane, such as the classical Steiner tree problem and...

Convex relaxation | Γ-convergence | Gilbert-steiner problem | Geometric measure theory | Optimal partitions | Calculus of variations | MATHEMATICS, APPLIED | geometric measure theory | MINIMIZATION | calculus of variations | optimal partitions | Gilbert-Steiner problem | Gamma-convergence | convex relaxation | SCHEMES | Mathematics | Optimization and Control

Convex relaxation | Γ-convergence | Gilbert-steiner problem | Geometric measure theory | Optimal partitions | Calculus of variations | MATHEMATICS, APPLIED | geometric measure theory | MINIMIZATION | calculus of variations | optimal partitions | Gilbert-Steiner problem | Gamma-convergence | convex relaxation | SCHEMES | Mathematics | Optimization and Control

Journal Article

Discrete Mathematics, ISSN 0012-365X, 08/2012, Volume 312, Issue 15, pp. 2349 - 2355

In an undirected or a directed graph, the edge-connectivity between two disjoint vertex sets X and Y is defined as the minimum number of edges or arcs that...

Edge-connectivity | Graph orientation | Group Steiner tree packing | MATHEMATICS

Edge-connectivity | Graph orientation | Group Steiner tree packing | MATHEMATICS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2016, Volume 368, Issue 10, pp. 7153 - 7188

k if \Vert\sum _{i\in I}\mathbold {x}_i\Vert\leq 1-element subsets I\subseteq \{1,2,\dots ,m\} \overline {\mathcal {C}}(k,d)-collapsing family of unit vectors...

STEINER PROBLEM | MATHEMATICS | PROOF | SPACES | BOUNDS | MATRICES

STEINER PROBLEM | MATHEMATICS | PROOF | SPACES | BOUNDS | MATRICES

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 12, pp. 4205 - 4207

Suppose that G is a simple graph. Let g ( G ) and s ( G ) be the geodetic number and the Steiner number of G , respectively. In this note, we prove that, for...

Steiner tree | Geodetic set | Steiner set | MATHEMATICS | NUMBER

Steiner tree | Geodetic set | Steiner set | MATHEMATICS | NUMBER

Journal Article

34.
Full Text
Approximation Algorithms for Highly Connected Multi-dominating Sets in Unit Disk Graphs

Algorithmica, ISSN 0178-4617, 11/2018, Volume 80, Issue 11, pp. 3270 - 3292

Given an undirected graph on a node set V and positive integers k and m, a k-connected m-dominating set ((k, m)-CDS) is defined as a subset S of V such that...

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Connected dominating set | Mathematics of Computing | Computer Science | Theory of Computation | Approximation algorithm | Algorithm Analysis and Problem Complexity | Unit disk graph | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | WEIGHTED STEINER TREES | AD HOC | WIRELESS NETWORKS

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Connected dominating set | Mathematics of Computing | Computer Science | Theory of Computation | Approximation algorithm | Algorithm Analysis and Problem Complexity | Unit disk graph | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | WEIGHTED STEINER TREES | AD HOC | WIRELESS NETWORKS

Journal Article

Journal of Economic Theory, ISSN 0022-0531, 2008, Volume 140, Issue 1, pp. 27 - 65

This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to...

Imprecision aversion | Imprecise information | Steiner point | Multiple priors | DEFINITION | AMBIGUITY AVERSION | imprecise information | steiner point | DECISION-MAKING | imprecision aversion | PREFERENCES | AXIOMS | multiple priors | UNCERTAINTY AVERSION | ECONOMICS | UTILITY | Economics and Finance | Humanities and Social Sciences

Imprecision aversion | Imprecise information | Steiner point | Multiple priors | DEFINITION | AMBIGUITY AVERSION | imprecise information | steiner point | DECISION-MAKING | imprecision aversion | PREFERENCES | AXIOMS | multiple priors | UNCERTAINTY AVERSION | ECONOMICS | UTILITY | Economics and Finance | Humanities and Social Sciences

Journal Article

Ars Combinatoria, ISSN 0381-7032, 04/2017, Volume 132, pp. 219 - 229

For vertices u, v in a connected graph G, a u - v chordless path in G is a u v monophonic path. The monophonic interval J(G)[u, v] consists of all vertices...

Monophonic number | Monophonic path | Extreme monophonic graph | Open monophonic number | Monophonic set | monophonic path | MATHEMATICS | monophonic number | extreme monophonic graph | open monophonic number | STEINER | monophonic set | GEODETIC NUMBER

Monophonic number | Monophonic path | Extreme monophonic graph | Open monophonic number | Monophonic set | monophonic path | MATHEMATICS | monophonic number | extreme monophonic graph | open monophonic number | STEINER | monophonic set | GEODETIC NUMBER

Journal Article

Lecture Notes in Electrical Engineering, ISSN 1876-1100, 2018, Volume 423, pp. 373 - 381

Conference Proceeding

Graphs and Combinatorics, ISSN 0911-0119, 1/2012, Volume 28, Issue 1, pp. 77 - 84

Geodesic convex sets, Steiner convex sets, and J-convex (alias induced path convex) sets of lexicographic products of graphs are characterized. The geodesic...

05C76 | Convex sets | 05C12 | Steiner sets | Mathematics | Engineering Design | Combinatorics | Lexicographic product of graphs | MATHEMATICS | NUMBERS | STEINER INTERVALS | TRANSIT FUNCTION | PATH CONVEXITY | Universities and colleges | Geodetics | Graphs | Theorems | Combinatorial analysis

05C76 | Convex sets | 05C12 | Steiner sets | Mathematics | Engineering Design | Combinatorics | Lexicographic product of graphs | MATHEMATICS | NUMBERS | STEINER INTERVALS | TRANSIT FUNCTION | PATH CONVEXITY | Universities and colleges | Geodetics | Graphs | Theorems | Combinatorial analysis

Journal Article

39.
Brunn-Minkowski inequality for the 1-Riesz capacity and level set convexity for the 1/2-Laplacian

Journal of Convex Analysis, ISSN 0944-6532, 2015, Volume 22, Issue 4, pp. 1125 - 1134

We prove that that the 1-Riesz capacity satisfies a Brunn-Minkowski inequality, and that the capacitary function of the 1/2-Laplacian is level set convex.

Riesz capacity | Brunn-Minkowski inequality | Fractional Laplacian | Level set convexity | level set convexity | MATHEMATICS | STEINER SYMMETRIZATION

Riesz capacity | Brunn-Minkowski inequality | Fractional Laplacian | Level set convexity | level set convexity | MATHEMATICS | STEINER SYMMETRIZATION

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2017, Volume 305, pp. 1268 - 1319

We study existence and partial regularity relative to the weighted Steiner problem in Banach spaces. We show C1 regularity almost everywhere for almost...

Geometric measure theory | Steiner problem | MATHEMATICS | CURVE REGULARITY | Metric Geometry | Mathematics | Classical Analysis and ODEs

Geometric measure theory | Steiner problem | MATHEMATICS | CURVE REGULARITY | Metric Geometry | Mathematics | Classical Analysis and ODEs

Journal Article

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