1

June 2017
Discrete & Computational Geometry: Volume 57 Issue 4, June 2017

**Publisher:** Springer-Verlag New York, Inc.

In this note we prove that for any compact subset S of a Busemann surface $$({{\mathcal {S}}},d)$$(S,d) (in particular, for any simple polygon with geodesic metric) and any positive number $$\delta $$ź, the minimum number of closed balls of radius $$\delta $$ź with centers at $${\mathcal {S}}$$S and covering the ...

**Keywords**:
Balls, Busemann surfaces, Covering numbers, Packing number

2

January 2015
Discrete & Computational Geometry: Volume 53 Issue 1, January 2015

**Publisher:** Springer-Verlag New York, Inc.

In this paper, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into $$L_1$$L1. As a corollary, we obtain that all planar graphs which are 1-skeletons of planar non-positively curved complexes with regular Euclidean polygons as cells are $$L_1$$L1-embeddable with distortion at most $$2$$2. Our ...

**Keywords**:
Non-positive curvature, Isometric embedding, CAT(0) surfaces, Distortion, Planar embedding

3

October 2014
ACM Transactions on Algorithms (TALG): Volume 11 Issue 2, November 2014

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 2

Downloads (6 Weeks): 0, Downloads (12 Months): 14, Downloads (Overall): 155

Full text available:

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The Directed Steiner Tree (DST) problem is a cornerstone problem in network design. We focus on the generalization of the problem with higher connectivity requirements. The problem with one root and two sinks is APX-hard. The problem with one root and many sinks is as hard to approximate as the ...

**Keywords**:
rooted connectivity, network design, approximation algorithms, graph connectivity, Hardness of approximation

4

July 2013
ICALP'13: Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I

**Publisher:** Springer-Verlag

We consider the approximability of the maximum edge-disjoint paths problem (MEDP) in undirected graphs, and in particular, the integrality gap of the natural multicommodity flow based relaxation for it. The integrality gap is known to be $\Omega(\sqrt{n})$ even for planar graphs [11] due to a simple topological obstruction and a ...

5

December 2012
WINE'12: Proceedings of the 8th international conference on Internet and Network Economics

**Publisher:** Springer-Verlag

The second welfare theorem tells us that social welfare in an economy can be maximized at an equilibrium given a suitable redistribution of the endowments. We examine welfare maximization without redistribution. Specifically, we examine whether the clustering of traders into k submarkets can improve welfare in a linear exchange economy. ...

6

February 2012
Mathematical Programming: Series A and B: Volume 131 Issue 1-2, February 2012

**Publisher:** Springer-Verlag New York, Inc.

We prove the NP-completeness of the integer multiflow problem in planar graphs, with the following restrictions: there are only two classes of parallel demand edges, both lying on the infinite face of the routing graph. This was one of the open challenges concerning disjoint paths, explicitly asked by Müller (Math ...

**Keywords**:
Integer multiflows, Planar graphs, Disjoint paths, 05C38

7

February 2012
Mathematical Programming: Series A and B: Volume 131 Issue 1-2, February 2012

**Publisher:** Springer-Verlag New York, Inc.

We prove the NP-completeness of the integer multiflow problem in planar graphs, with the following restrictions: there are only two classes of parallel demand edges, both lying on the infinite face of the routing graph. This was one of the open challenges concerning disjoint paths, explicitly asked by Müller (Math ...

**Keywords**:
Disjoint paths, Planar graphs

8

January 2012
SODA '12: Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms

**Publisher:** Society for Industrial and Applied Mathematics

**Bibliometrics**:

Citation Count: 7

Downloads (6 Weeks): 0, Downloads (12 Months): 6, Downloads (Overall): 112

Full text available:

PDF
The Directed Steiner Tree (DST) problem is a cornerstone problem in network design. We focus on the generalization of the problem with higher connectivity requirements. The problem with one root and two sinks is APX-hard. The problem with one root and many sinks is as hard to approximate as the ...

9

September 2010
APPROX/RANDOM'10: Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques

**Publisher:** Springer-Verlag

We consider the question: What is the maximum flow achievable in a network if the flow must be decomposable into a collection of edge-disjoint paths? Equivalently, we wish to find a maximum weighted packing of disjoint paths, where the weight of a path is the minimum capacity of an edge ...