Publications related to On approximation algorithms and polyhedral relaxations for knapsack problems, and clustered planarity testing

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Drawing Planar Graphs Of Bounded Degree With Few Slopes

János Pach, Balázs Keszegh, Doemoetoer Palvoelgyi

We settle a problem of Dujmovic, Eppstein, Suderman, and Wood by showing that there exists a function f with the property that every planar graph G with maximum degree d admits a drawing with noncrossing straight-line edges, using at most f(d) different sl ...

Siam Publications2013

Steiner Tree Approximation via Iterative Randomized Rounding

Thomas Rothvoss, Laura Sanità

The Steiner tree problem is one of the most fundamental NP-hard problems: given a weighted undirected graph and a subset of terminal nodes, find a minimum-cost tree spanning the terminals. In a sequence of papers, the approximation ratio for this problem w ...

Assoc Computing Machinery2013

The School Bus Problem on Trees

Laura Sanità, Adrian Aloysius Bock

The School Bus Problem is an NP-hard vehicle routing problem in which the goal is to route buses that transport children to a school such that for each child, the distance travelled on the bus does not exceed the shortest distance from the child's home to ...

Springer US2013

On The Queue Number Of Planar Graphs

János Pach, Fabrizio Frati

We prove that planar graphs have O(log(2) n) queue number, thus improving upon the previous O(root n) upper bound. Consequently, planar graphs admit three-dimensional straight-line crossing-free grid drawings in O(n log(8) n) volume, thus improving upon th ...

Siam Publications2013

Fabrication-aware Design with Intersecting Planar Pieces

Mark Pauly, Yuliy Gennadievich Schwartzburg

We propose a computational design approach to generate 3D models composed of interlocking planar pieces. We show how intricate 3D forms can be created by sliding the pieces into each other along straight slits, leading to a simple construction that does no ...

Blackwell Publishing2013

Supercriticality of an annealed approximation of Boolean networks

Thomas Mountford, Daniel Rodrigues Valesin

We consider a model recently proposed by Chatterjee and Durrett [1] as an "annealed approximation" of boolean networks, which are a class of cellular automata on a random graph, as defined by S. Kauffman [5]. The starting point is a random directed graph o ...

Univ Washington, Dept Mathematics2013

Santa Claus Schedules Jobs On Unrelated Machines

Ola Nils Anders Svensson

One of the classic results in scheduling theory is the 2-approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines; i.e., job j requires time p(ij) if processed on machine i. More t ...

Siam Publications2012

Lower bounds on the obstacle number of graphs

János Pach, Doemoetoer Palvoelgyi, Padmini Mukkamala

Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices of G are joined by an edge if and only if the corresponding points can be con ...

2012

On approximation algorithms and polyhedral relaxations for knapsack problems, and clustered planarity testing

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Single machine scheduling with scenarios

Drawing Planar Graphs Of Bounded Degree With Few Slopes

Decomposition and tractability in qualitative spatial and temporal reasoning

Steiner Tree Approximation via Iterative Randomized Rounding

The School Bus Problem on Trees

On The Queue Number Of Planar Graphs

Fabrication-aware Design with Intersecting Planar Pieces

Supercriticality of an annealed approximation of Boolean networks

Santa Claus Schedules Jobs On Unrelated Machines

Lower bounds on the obstacle number of graphs

Single machine scheduling with scenarios

Drawing Planar Graphs Of Bounded Degree With Few Slopes

The School Bus Problem on Trees

Supercriticality of an annealed approximation of Boolean networks

Decomposition and tractability in qualitative spatial and temporal reasoning

Steiner Tree Approximation via Iterative Randomized Rounding

Fabrication-aware Design with Intersecting Planar Pieces

On The Queue Number Of Planar Graphs

Lower bounds on the obstacle number of graphs

Santa Claus Schedules Jobs On Unrelated Machines