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AllPairs Bottleneck Paths in Vertex Weighted Graphs
 In Proc. of SODA, 978–985
, 2007
"... Let G = (V, E, w) be a directed graph, where w: V → R is an arbitrary weight function defined on its vertices. The bottleneck weight, or the capacity, of a path is the smallest weight of a vertex on the path. For two vertices u, v the bottleneck weight, or the capacity, from u to v, denoted c(u, v), ..."
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Cited by 9 (1 self)
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vertex weights. The APBP problem has numerous applications, and several interesting problems that have recently attracted attention can be reduced to it, with no asymptotic loss in the running times of the known algorithms for these problems. Some examples are a result of Vassilevska and Williams [STOC
Counting thin subgraphs via packings faster than meetinthemiddle time
 In SODA
, 2014
"... Abstract. Vassilevska and Williams (STOC 2009) showed how to count simple paths on k vertices and matchings on k/2 edges in an nvertex graph in time nk/2+O(1). In the same year, two different algorithms with the same runtime were given by Koutis and Williams (ICALP 2009), and Björklund et al. (ESA ..."
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Cited by 2 (1 self)
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Abstract. Vassilevska and Williams (STOC 2009) showed how to count simple paths on k vertices and matchings on k/2 edges in an nvertex graph in time nk/2+O(1). In the same year, two different algorithms with the same runtime were given by Koutis and Williams (ICALP 2009), and Björklund et al
More applications of the polynomial method to algorithm design
, 2015
"... In lowdepth circuit complexity, the polynomial method is a way to prove lower bounds by translating weak circuits into lowdegree polynomials, then analyzing properties of these polynomials. Recently, this method found an application to algorithm design: Williams (STOC 2014) used it to compute all ..."
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Cited by 3 (2 self)
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In lowdepth circuit complexity, the polynomial method is a way to prove lower bounds by translating weak circuits into lowdegree polynomials, then analyzing properties of these polynomials. Recently, this method found an application to algorithm design: Williams (STOC 2014) used it to compute
3SUM, 3XOR, Triangles
, 2013
"... We show that if one can solve 3SUM on a set of size n in time n1+ɛ then one can list t triangles in a graph with m edges in time Õ(m1+ɛt1/3+ɛ ′ ) for any ɛ ′> 0. This is a reversal of Pǎtra¸scu’s reduction from 3SUM to listing triangles (STOC ’10). We then reexecute both Pǎtra¸scu’s reduction an ..."
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Cited by 3 (0 self)
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We show that if one can solve 3SUM on a set of size n in time n1+ɛ then one can list t triangles in a graph with m edges in time Õ(m1+ɛt1/3+ɛ ′ ) for any ɛ ′> 0. This is a reversal of Pǎtra¸scu’s reduction from 3SUM to listing triangles (STOC ’10). We then reexecute both Pǎtra¸scu’s reduction
On the Lossiness of the Rabin Trapdoor Function
, 2013
"... Abstract. Lossy trapdoor functions, introduced by Peikert and Waters (STOC ’08), are functions that can be generated in two indistinguishable ways: either the function is injective, and there is a trapdoor to invert it, or the function is lossy, meaning that the size of its range is strictly smaller ..."
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Abstract. Lossy trapdoor functions, introduced by Peikert and Waters (STOC ’08), are functions that can be generated in two indistinguishable ways: either the function is injective, and there is a trapdoor to invert it, or the function is lossy, meaning that the size of its range is strictly
3sum hardness in (dynamic) data structures
 CoRR
"... We prove lower bounds for several (dynamic) data structure problems conditioned on the well known conjecture that 3SUM cannot be solved in O(n2−Ω(1)) time. This continues a line of work that was initiated by Pǎtraşcu [STOC 2010] and strengthened recently by Abboud and VassilevskaWilliams [FOCS 20 ..."
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Cited by 2 (1 self)
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We prove lower bounds for several (dynamic) data structure problems conditioned on the well known conjecture that 3SUM cannot be solved in O(n2−Ω(1)) time. This continues a line of work that was initiated by Pǎtraşcu [STOC 2010] and strengthened recently by Abboud and VassilevskaWilliams [FOCS