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The bidimensional theory of boundedgenus graphs
 SIAM Journal on Discrete Mathematics
, 2004
"... 1 Introduction The recent theory of fixedparameter algorithms and parameterized complexity [13] has attracted much attention in its less than 10 years of existence. In general the goal is to understand when NPhard problems have algorithms thatare exponential only in a parameter k of the problem i ..."
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Cited by 16 (8 self)
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1 Introduction The recent theory of fixedparameter algorithms and parameterized complexity [13] has attracted much attention in its less than 10 years of existence. In general the goal is to understand when NPhard problems have algorithms thatare exponential only in a parameter k of the problem instead of the problemsize n. Fixedparameter algorithms whose running time is polynomial for fixedparameter valuesor more precisely
Polynomialtime approximation schemes for subsetconnectivity problems in boundedgenus graphs
, 2009
"... We present the first polynomialtime approximation schemes (PTASes) for the following subsetconnectivity problems in edgeweighted graphs of bounded genus: Steiner tree, lowconnectivity survivablenetwork design, and subset TSP. The schemes run in O(n log n) time for graphs embedded on both orien ..."
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Cited by 18 (4 self)
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orientable and nonorientable surfaces. This work generalizes the PTAS frameworks of Borradaile, Klein, and Mathieu [BMK07, Kle06] from planar graphs to boundedgenus graphs: any future problems shown to admit the required structure theorem for planar graphs will similarly extend to boundedgenus graphs.
Fully dynamic algorithms for bounded genus graphs
, 1997
"... We present a deterministic algorithm that maintains the connected components of a graph as edges are inserted and deleted, provided the genus of the graph is bounded by a fixed constant. The algorithm runs in O(log2 n) amortized time per insertion, O(log3 n) amortized time per deletion, and O(log n ..."
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We present a deterministic algorithm that maintains the connected components of a graph as edges are inserted and deleted, provided the genus of the graph is bounded by a fixed constant. The algorithm runs in O(log2 n) amortized time per insertion, O(log3 n) amortized time per deletion, and O
Probabilistic embeddings of bounded genus graphs into planar graphs
 Proc. 23rd Ann. ACM Symp. Comput. Geom
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Cited by 17 (5 self)
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Subexponential Parameterized Algorithms on BoundedGenus Graphs and HMinorFree Graphs
"... cfl 202005 ACM 00045411/202005/0100100001 $5.00 ..."
Multicuts in Planar and BoundedGenus Graphs with Bounded Number of Terminals
, 2015
"... Given an undirected, edgeweighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimumweight set of edges such that, after deleting these edges, the two terminals of each pair belong to different connected components of the graph. Rely ..."
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Given an undirected, edgeweighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimumweight set of edges such that, after deleting these edges, the two terminals of each pair belong to different connected components of the graph
LinearTime Compression of BoundedGenus Graphs into InformationTheoretically Optimal
, 2014
"... ar ..."
An algorithm for finding an induced cycle in planar graphs and bounded genus graphs
"... In this paper, we consider the problem of finding an induced cycle passing through k given vertices, which we call the induced cycle problem. The significance of finding induced cycles stems from the fact that precise characterization of perfect graphs would require structures of graphs without an o ..."
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Cited by 14 (1 self)
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to graphs embedded in a fixed surface. We note that the linear time algorithm (the second result) is independent from the first result. Let us point out that we give the first polynomial time algorithm for the problem for the bounded genus case. In fact, our proof gives a short proof of a result announced
Probabilistic Embeddings of Bounded Genus Graphs IntoPlanar Graphs
"... ABSTRACT A probabilistic Cembedding of a (guest) metric M into a collection of (host) metrics M01,..., M0k is a randomized mapping F of M into one of the M01,..., M0k such that, for any two points p, q in the guest metric: 1. The distance between F (p) and F (q) in any M 0i is not smaller than the ..."
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ABSTRACT A probabilistic Cembedding of a (guest) metric M into a collection of (host) metrics M01,..., M0k is a randomized mapping F of M into one of the M01,..., M0k such that, for any two points p, q in the guest metric: 1. The distance between F (p) and F (q) in any M 0i is not smaller than the original distance between p and q. 2. The expected distance between F (p) and F (q) in (random) M0i is not greater than some constant C times the original distance, for C> = 1. The constant C is called the distortion of the embedding. Lowdistortion probabilistic embeddings enable reducing algorithmic problems over "hard " guest metrics into "easy " host metrics.
Lineartime compression of boundedgenus graphs into informationtheoretically optimal number of bits
 In: 13th Symposium on Discrete Algorithms (SODA
, 2002
"... 1 I n t roduct ion This extended abstract summarizes a new result for the graph compression problem, addressing how to compress a graph G into a binary string Z with the requirement that Z can be decoded to recover G. Graph compression finds important applications in 3D model compression of Computer ..."
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Cited by 17 (1 self)
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additive function fl(n) with log 2 N~(n) < fl(n) + o(fl(n)). Our methodology is applicable to general classes of graphs; this extended abstract focuses on graphs with sublinear genus. 2 For example, if the input nnode,rgraph G is equipped with an embedding on its genus surface, which is a reasonable assumption
Results 1  10
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22,725