32847785
Approximation Algorithms for Independent Sets in Map Graphs
This paper presents polynomial-time approximation algorithms for the problem of computing a maximum independent set in a given map graph G with or without weights on its vertices. If G is given together with a map, then a ratio of 1+? can be achieved by a quadratic-time algorithm for any given constant ??0, no matter whether each vertex of G is given a weight or not. In case G is given without a map, a ratio of 4 can be achieved by a low-degree polynomial-time algorithm if no vertex is given a weight, while a ratio of 5 can be achieved by a low-degree polynomial-time algorithm otherwise.
38006851
Approximation Algorithms for Independent Sets in Map Graphs
This paper presents polynomial-time approximation algorithms for the problem of computing a maximum independent set in a given map graph G with or without weights on its vertices. If G is given together with a map, then a ratio of 1+δ can be achieved in O(n2) time for any given constant δ > 0, no matter whether each vertex of G is given a weight or not. In case G is given without a map, a ratio of 4 can be achieved in O(n7) time if no vertex is given a weight, while a ratio of O(log n) can be achieved in O(n7 log n) time otherwise. Behind the design of our algorithms are several fundamental results for map graphs; these results can be used to design good approximation algorithms for coloring and vertex cover in map graphs, and may find applications to other problems on map graphs as well.
20004613
Disk Embeddings of Planar Graphs
Abstract 
Given a planar graph $G=(V,E)$ and a rooted forest ${\FF}=(V_{\FF}, A_{\FF})$ 
with leaf set $V$, we wish to decide whether $G$ has a plane embedding $\GG$ 
satisfying the following condition: There are $|V_{\FF}|-|V|$ pairwise noncrossing 
Jordan curves in the plane one-to-one corresponding to the nonleaf vertices of 
${\FF}$ such that for every nonleaf vertex $f$ of ${\FF}$, the interior of the curve 
$\JJ_f$ corresponding to $f$ contains all the leaf descendants of $f$ in ${\FF}$
but contains no other leaves of ${\FF}$. 
This problem arises from theoretical studies in geographic database systems. 
It is unknown whether this problem can be solved in polynomial time. 
This paper presents an almost linear-time algorithm for a nontrivial special case 
where the set of leaf descendants of each nonleaf vertex $f$ in ${\FF}$ induces 
a connected subgraph of $G$. 


41188840
Finding Double Euler Trails of Planar Graphs in Linear Time
This paper answers an open question in the design of complimentary metal-oxide semiconductor VLSI circuits. The question asks whether a polynomial-time algorithm can decide if a given planar graph has a plane embedding ${\cal E}$ such that ${\cal E}$ has an Euler trail P = e1 e2 ... em and its dual graph has an Euler trail $P^*=e^*_1 e^*_2 \ldots e^*_m$, where $e^*_i$ is the dual edge of ei for i=1,2,...,m. This paper answers this question in the affirmative by presenting a linear-time algorithm.
701
Common-Face Embeddings of Planar Graphs
Given a planar graph $\Ggg$ and a sequence ${\CC}_1,\ldots,{\CC}_q$, where each ${\CC}_i$ is a family of vertex subsets of $\Ggg$, we wish to find a plane embedding of $\Ggg$, if any exists, such that, for each $i\in\{1,\ldots,q\}$, there is a face Fi in the embedding whose boundary contains at least one vertex from each set in CCi. This problem has applications in the recovery of topological information from geographical data and the design of constrained layouts in VLSI. Let $\inputsize$ be the input size, i.e., the total number of vertices and edges in $\Ggg$ and the families CCi, counting multiplicity. We show that this problem is NP-complete in general. We also show that it is solvable in $O(\inputsize\log \inputsize)$ time for the special case in which, for each input family CCi, each set in CCi induces a connected subgraph of the input graph $\Ggg$. Note that the classical problem of simply finding a planar embedding is a further special case of this case with q=0. Therefore, the processing of the additional constraints CC1, . . .,CCq incurs only a logarithmic factor of overhead.
7399730
An Almost Linear Time 2.8334-Approximation Algorithm for the Disc Covering Problem
The disc covering problem asks to cover a set of points on the plane with a minimum number of fix-sized discs. We develop an O(n(logn)2(loglogn)2) deterministic time 2.8334-approximation algorithm for this problem. Previous approximation algorithms [7,3,6], when used to achieve the same approximation ratio for the disc covering problem, will have much higher time complexity than our algorithms.
27700138
Improved single-video-object rate control for MPEG-4
Rate control plays a central role in constant bit-rate video coding applications using MPEG-4. This paper considers single-video-object rate control for MPEG-4 and presents a new rate-control algorithm based on the quadratic rate-distortion (R-D) model. The major innovations are a novel constraint for the least-mean-square estimation of the model parameters of the R-D function, a new measure for the encoding complexity, novel quantizer control and an efficient frame skipping strategy. Simulation results show that the MPEG-4 coder, using the proposed algorithm, can achieve a higher PSNR than a coder using the conventional rate-control algorithm.
9224231
The plain old television in a smart apartment
Our GO (www.go-outside.org) project focuses on community access for the cognitively impaired population. In addition to devising new facilities, we are interested in using existing appliances found in an apartment to interact with a user to help with a specific task, e.g., making a trip to the doctor. This requires establishment of collaboration protocols between the appliances (and smart agents) and user to be established. These protocols must enforce certain safety properties, e.g., that the user get timely information to start a task. We will show how we use a light-weight formal modeling toolkit to reason about a protocol's ability to meet safety properties
7983044
Algorithm-based checkpoint-free fault tolerance for parallel matrix computations on volatile resources
As the size of today's high performance computers increases from hundreds, to thousands, and even tens of thousands of processors, node failures in these computers are becoming frequent events. Although checkpoint/rollback-recovery is the typical technique to tolerate such failures, it often introduces a considerable overhead. Algorithm-based fault tolerance is a very cost-effective method to incorporate fault tolerance into matrix computations. However, previous algorithm-based fault tolerance methods for matrix computations are often derived using algorithms that are seldomly used in the practice of today's high performance matrix computations and have mostly focused on platforms where failed processors produce incorrect calculations. To fill this gap, this paper extends the existing algorithm-based fault tolerance to the volatile computing platform where the failed processor stops working and applies it to scalable high performance matrix computations with two dimensional block cyclic data distribution. We show the practicality of this technique by applying it to the ScaLAPACK/PBLAS matrix-matrix multiplication kernel. Experimental results demonstrate that the proposed approach is able to survive process failures with a very low performance overhead
28595321
A PTAS for a Disc Covering Problem Using Width-Bounded Separators
In this paper, we study the following disc covering problem: Given a set of discs of various radii on the plane, find a subset of discs to maximize the area covered by exactly one disc. This problem originates from the application in digital halftoning, with the best known approximation factor being 5.83 [2]. We show that if the maximum radius is no more than a constant times the minimum radius, then there exists a polynomial time approximation scheme. Our techniques are based on the width-bounded geometric separator recently developed in [5,6].