Journal ArticleDOI
NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs
Harry B. Hunt,Madhav V. Marathe,Venkatesh Radhakrishnan,S. S. Ravi,Daniel J. Rosenkrantz,Richard Edwin Stearns +5 more
Reads0
Chats0
TLDR
The approximation schemes for hierarchically specified unit disk graphs presented in this paper are among the first approximation schemes in the literature for natural PSPACE-hard optimization problems.About:
This article is published in Journal of Algorithms.The article was published on 1998-02-01. It has received 345 citations till now. The article focuses on the topics: Indifference graph & Chordal graph.read more
Citations
More filters
Proceedings ArticleDOI
Geometric ad-hoc routing: of theory and practice
TL;DR: A new geometric routing algorithm is proposed which is outstandingly efficient on practical average-case networks, however is also in theory asymptotically worst-case optimal and the formerly necessary assumption that the distance between network nodes may not fall below a constant value is dropped.
Proceedings ArticleDOI
A clustering scheme for hierarchical control in multi-hop wireless networks
Suman Banerjee,Samir Khuller +1 more
TL;DR: This paper presents a clustering scheme to create a hierarchical control structure for multi-hop wireless networks and presents an efficient distributed implementation of the clustering algorithm for a set of wireless nodes to create the set of desired clusters.
Proceedings ArticleDOI
Complexity in geometric SINR
TL;DR: The first NP-completeness proofs in the geometric SINR model, which explicitly uses the fact that nodes are distributed in the Euclidean plane, are presented, which proves two problems to be NP-complete: Scheduling and One-Shot Scheduling.
Proceedings ArticleDOI
On the complexity of scheduling in wireless networks
TL;DR: It is shown that under a setting with single-hop traffic and no rate control, the maximal scheduling policy can achieve a constant fraction of the capacity region for networks whose connectivity graph can be represented using one of the above classes of graphs.
Journal ArticleDOI
Parameterized Complexity and Approximation Algorithms
TL;DR: The different ways parameterized complexity can be extended to approximation algorithms, survey results of this type and proposed directions for future research are discussed.
References
More filters
Journal ArticleDOI
Hierarchically specified unit disk graphs
TL;DR: Both PSPACE-hardness results and polynomial time approximations are presented for most of the problems considered, including minimum vertex coloring, maximum independent set, minimum clique cover, minimum dominating set and minimum independent dominating set.
Journal ArticleDOI
An approximation scheme for some Steiner tree problems in the plane
TL;DR: A polynomial-time approximation scheme for the Steiner tree problem in the plane when the given set of regular points is c-local, i.e., in the minimum-cost spanning tree for the givenSet of regular Points, where the length of the longest edge is at most c times thelength of the shortest edge.
Complexity of hierarchically and 1-dimensional periodically specified problems I: Hardness results.
TL;DR: It is proved that there is a polynomial time algorithm that given a 1-FPN- or 1- FPN(BC)specification of a graph, constructs a level-restricted L-specifying of an isomorphic graph (or formula) that provides alternative and unified proofs of many hardness results proved in the past.
Proceedings Article
Complexity of hierarchically and 1-dimensional periodically specified problems
TL;DR: In this paper, the complexity of various combinatorial and satisfiability problems when instances are specified using one of the following specifications: (1) the 1-dimensional finite periodic narrow specifications of Wanke and Ford et al. (2) the 2-way infinite1-dimensional narrow periodic specifications of Orlin et al., (3) the hierarchical specifications of Lengauer et al, and (4) the 3-dimensional CNF satisfiability problem of Schaefer.
Proceedings ArticleDOI
Approximation schemes for PSPACE-complete problems for succinct specifications (preliminary version)
TL;DR: Although many basic problems are PSPACE-hard even for level-restricted specifications of planar instances, it is shown that many of these basic problems II have efficient approximation algorithms with performance guarantees which are asymptotically equal to the best known performance guarantee for H for flat specification.