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130,604
SpaceEfficient Algorithms for Reachability in SurfaceEmbedded Graphs
, 2012
"... This work presents a logspace reduction which compresses a directed acyclic graph with m sources embedded on a surface of genus g to a graph on O(m + g) vertices while preserving reachability between a given pair of vertices. Applying existing algorithms to this smaller graph gives improved space b ..."
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bounds as well as improved simultaneous timespace bounds for the reachability problem for a large class of directed acyclic graphs. Specifically, it significantly extends the class of surfaceembedded graphs with logspace reachability algorithms: from planar graphs with O(log n) sources, to graphs
SpaceEfficient Algorithms for Reachability in SurfaceEmbedded Graphs
, 2012
"... This work presents a logspace reduction which compresses a directed acyclic graph with m sources embedded on a surface of genus g to a graph on O(m + g) vertices while preserving reachability between a given pair of vertices. Applying existing algorithms to this smaller graph gives improved space b ..."
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bounds as well as improved simultaneous timespace bounds for the reachability problem for a large class of directed acyclic graphs. Specifically, it significantly extends the class of surfaceembedded graphs with logspace reachability algorithms: from planar graphs with O(log n) sources, to graphs
SpaceEfficient Algorithms for Reachability in SurfaceEmbedded Graphs
, 2010
"... We consider the reachability problem for a certain class of directed acyclic graphs embedded on surfaces. Let G(m, g) be the class of directed acyclic graphs with m = m(n) source vertices embedded on a surface (orientable or nonorientable) of genus g = g(n). We give a logspace reduction that on in ..."
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Cited by 3 (1 self)
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We consider the reachability problem for a certain class of directed acyclic graphs embedded on surfaces. Let G(m, g) be the class of directed acyclic graphs with m = m(n) source vertices embedded on a surface (orientable or nonorientable) of genus g = g(n). We give a logspace reduction
Global Minimum Cuts in Surface Embedded Graphs
"... We give a deterministic algorithm to find the minimum cut in a surfaceembedded graph in nearlinear time. Given an undirected graph embedded on an orientable surface of genus g, our algorithm computes the minimum cut in g O(g) n log log n time, matching the running time of the fastest algorithm kno ..."
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Cited by 8 (5 self)
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We give a deterministic algorithm to find the minimum cut in a surfaceembedded graph in nearlinear time. Given an undirected graph embedded on an orientable surface of genus g, our algorithm computes the minimum cut in g O(g) n log log n time, matching the running time of the fastest algorithm
FAST ALGORITHMS FOR SURFACE EMBEDDED GRAPHS VIA HOMOLOGY
, 2013
"... We describe several results on combinatorial optimization problems for graphs where the input comes with an embedding on an orientable surface of small genus. While the specific techniques used differ between problems, all the algorithms we describe share one common feature in that they rely on the ..."
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We describe several results on combinatorial optimization problems for graphs where the input comes with an embedding on an orientable surface of small genus. While the specific techniques used differ between problems, all the algorithms we describe share one common feature in that they rely
Excluding Graphs as Immersions in Surface Embedded Graphs
"... We prove a structural characterization of graphs that forbid a fixed graph H as an immersion and can be embedded in a surface of Eüler genus γ. In particular, we prove that a graph G that excludes some connected graph H as an immersion and is embedded in a surface of Eüler genus γ has either “smal ..."
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We prove a structural characterization of graphs that forbid a fixed graph H as an immersion and can be embedded in a surface of Eüler genus γ. In particular, we prove that a graph G that excludes some connected graph H as an immersion and is embedded in a surface of Eüler genus γ has either
Computing Replacement Paths in Surface Embedded Graphs
 ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 2011
"... Let s and t be vertices in a directed graph G with nonnegative edge weights. The replacement paths problem asks us to compute, for each edge e in G, the length of the shortest path from s to t that does not traverse e. We describe an algorithm that solves the replacement paths problem for directed ..."
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Cited by 3 (0 self)
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graphs embedded on a surface of any genus g in O(gn log n) time, generalizing a recent O(n log n)time algorithm of WulffNilsen for planar graphs [SODA 2010].
Space Complexity of the Directed Reachability Problem over SurfaceEmbedded Graphs
, 2014
"... The graph reachability problem, the computational task of deciding whether there is a path between two given nodes in a graph is the canonical problem for studying space bounded computations. Three central open questions regarding the space complexity of the reachability problem over directed gra ..."
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breakthrough. We will discuss some of the recent progress reported on these questions for certain subclasses of surfaceembedded directed graphs.
AllPairs Minimum Cuts in NearLinear Time for SurfaceEmbedded Graphs
"... For an undirected nvertex graph G with nonnegative edgeweights, we consider the following type of query: given two vertices s and t in G, what is the weight of a minimum stcut in G? We solve this problem in preprocessing time O(n log3 n) for graphs of bounded genus, giving the first subquadrati ..."
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For an undirected nvertex graph G with nonnegative edgeweights, we consider the following type of query: given two vertices s and t in G, what is the weight of a minimum stcut in G? We solve this problem in preprocessing time O(n log3 n) for graphs of bounded genus, giving the first sub
Accepted Manuscript
, 2014
"... Covering nearly surfaceembedded graphs with a fixed number of balls ..."
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Covering nearly surfaceembedded graphs with a fixed number of balls
Results 1  10
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130,604