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
Book ChapterDOI
An Approximation Scheme for Some Steiner Tree Problems in the Plane
Tao Jiang,Lusheng Wang +1 more
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 and works for both Euclidean and rectilinear metrics.
Book ChapterDOI
Efficient parallel algorithms for shortest paths in planar graphs
Grammati Pantziou,Grammati Pantziou,Paul G. Spirakis,Paul G. Spirakis,Paul G. Spirakis,Christos D. Zaroliagis,Christos D. Zaroliagis +6 more
TL;DR: Efficient parallel algorithms are presented, on the CREW PRAM model, for generating a succinct encoding of all pairs shortest path information in a directed planar graph G with real-valued edge costs but no negative cycles.
Approximation algorithms for maximum two-dimensional pattern matching
TL;DR: In this paper, the problem of finding the maximum number of non-overlapping occurrences of the pattern in the text was introduced and polynomial time approximation algorithms and approximation schemes for this problem were devised.
Proceedings Article
Level-treewidth property, exact algorithms and approximation schemes
TL;DR: The level-treewidth property (LT-property) as mentioned in this paper is defined as the property of a graph such that the subgraph induced by the vertices in k-consecutive levels in the layout has treewidth O(f (k)), for some function f.
Journal ArticleDOI
The Auto- and Cross-Correlations of Walsh Functions
TL;DR: In this article, the correlations of Walsh functions are defined and some of their properties derived, including a recursion relation, which relates correlations of high index functions to those of low index functions.