Contiguous Cake Cutting: Hardness Results and Approximation Algorithms

13 Cake Cutting Algorithms

Imagine a cake that must be divided between a group of gluttonous children. To complicate matters, the cake is heterogeneous: two pieces of cake may differ in terms of their toppings, so the children have different preferences over the pieces (one may weakly prefer a larger proportion of chocolate curls, while another may single-mindedly desire the piece with the cherry). In this chapter we dis...

Cake Cutting Algorithms

Approximation algorithms and hardness results for the clique packing problem

For a fixed family F of graphs, an F -packing in a graphG is a set of pairwise vertex-disjoint subgraphs of G, each isomorphic to an element of F . Finding an F -packing that maximizes the number of covered edges is a natural generalization of the maximum matching problem, which is just F = {K2}. In this paper we provide new approximation algorithms and hardness results for the Kr-packing probl...

Approximation Algorithms and Hardness Results for Labeled Connectivity Problems

Let G = (V, E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function L : E → N. In addition, each label ` ∈ N has a non-negative cost c(`). The minimum label spanning tree problem (MinLST) asks to find a spanning tree in G that minimizes the overall cost of the labels used by its edges. Equivalently, we aim at finding a minimum cost subset of ...

Approximation algorithms and the hardness of approximation

Chandra Chekuri (Dept. of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL), Joseph Cheriyan (Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, ON), Ryan O’Donnell (School of Computer Science, Carnegie Mellon University, Pittsburgh, PA), Mohammad R. Salavatipour (Dept. of Computing Science, University of Alberta, Edmonton, AL), David Williamson (...