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Dynamic Bridge-Finding in Õ(log2 n) Amortized Time
[chapter]

2018
*
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
*

We support updates

doi:10.1137/1.9781611975031.3
dblp:conf/soda/HolmRT18
fatcat:7i7ehjmdzjdxbm26tzy72rfe5q
*in**O*((log*n*) 2 )*amortized**time*, and can*find*a*bridge**in*the component of any given vertex, or a*bridge*separating any two given vertices,*in**O*(log*n*/ log log*n*) worst case*time*. ... The previous best*dynamic**bridge**finding*was an*O*((log*n*) 3 )*amortized**time*algorithm by Thorup [STOC2000], which was a bittrick-based improvement on the*O*((log*n*) 4 )*amortized**time*algorithm by Holm ... and deletions of edges*in**O*((log*n*) 3 log log*n*)*amortized**time*,*find**bridges*and determine connected component sizes*in**O*(log*n*) worst-case*time*, and*find*2-edge connected component sizes*in**O*((log*n*...##
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Persistence, Amortization and Randomization

1991
*
ACM-SIAM Symposium on Discrete Algorithms
*

We show how to make some new data structures, including disjoint-set union-

dblp:conf/soda/DietzR91
fatcat:f5a4pr63tzgqrivh7fu7ql3fiu
*find*, partially persistent*in*optimal*time*and space. We eliminate*amortization*from*dynamic*fractional cascading. ... We show how to eliminate*amortization*from one of the data structures of Driscoll et. al. [9]. ... ~c A(w) is a proper union, split and*find**in**O*(loglog*n*)*time*. ...##
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Dynamic Planar Point Location in External Memory

2019
*
International Symposium on Computational Geometry
*

Our data structure supports queries

doi:10.4230/lipics.socg.2019.52
dblp:conf/compgeom/MunroN19
fatcat:ro5wyylxyjgxtcqef5dz5fx4b4
*in**O*(log B*n*(log log B*n*) 3 )) I/Os and updates*in**O*(log B*n*(log log B*n*) 2 ))*amortized*I/Os, where*n*is the number of segments*in*the subdivision and B is the block ... This is the first*dynamic*data structure with almost-optimal query cost. For comparison all previously known results for this problem require*O*(log 2 B*n*) I/Os to answer queries. ... The currently best data structure [13] achieves 1*O*(log*n*) query*time*and*O*(log 1+ε*n*) update*time*or*O*(log 1+ε*n*) query*time*and*O*(log*n*) update*time*; the best query-update trade-off described*in*[ ...##
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DYNAMIZATION OF THE TRAPEZOID METHOD FOR PLANAR POINT LOCATION IN MONOTONE SUBDIVISIONS

1992
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International journal of computational geometry and applications
*

Let

doi:10.1142/s0218195992000184
fatcat:utnmrf2nvfaqtlk5mej7xfq6k4
*n*be the current number of vertices of the subdivision. Point location queries take*O*(log*n*)*time*, while updates take*O*(*log2**n*)*time*. The space requirement is*O*(nlogn). ... We present a fully*dynamic*data structure for point location*in*a monotone sub division, based on the trapezoid method. ... Finally, for triangulations, one can achieve*O*(*n*) space and a tradeoff between query and update*time*; for example,*O*( (*log2**n*) jlog log*n*) query*time*and*O*( (1og3*n*) jlog log*n*) update*time*, or*O*(1og ...##
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Parallel Tree Contraction Part 2: Further Applications

1991
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SIAM journal on computing (Print)
*

To see that the above algorithm works

doi:10.1137/0220070
fatcat:i7bjji4aefes5ayetgrt2ywdfq
*in**O*(*log2**n*)*time*, simply note that each RAKE takes at most*O*(1og*n*)*time*and that CONTRACT is applied at most*O*(1og*n*)*times*by the results of [29] 0 THEOREM 2 ... This motivates another generalization of Parallel Free Contraction which will be used to compute the 3-connected components of a graph*in**O*(1ogn)*time*, instead of*O*(*log2**n*)*time*. ...##
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Consecutive interval query and dynamic programming on intervals

1998
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Discrete Applied Mathematics
*

Given a set of

doi:10.1016/s0166-218x(98)00021-3
fatcat:4pfauas4wzfqhknfrfxm55khdu
*n*points (nodes) on a line and a set of m weighted intervals defined on the nodes, we consider a particular*dynamic*programming (DP) problem on these intervals. ... If the weight function of the DP has convex or concave property, we can solve this DP problem efficiently by using matrix searching*in*Monge matrices, together with a new query data structure, which we ... Since each Bi has*O*(log'n) consecutive columns, all column minima*in*Bi can be computed*in**O*((gA(hi) -gA(h(i -1)) +*log2**n*)(log log*n*)2)*time*by applying the naive divide-andconquer algorithm. ...##
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Data structures for two-edge connectivity in planar graphs

1994
*
Theoretical Computer Science
*

There are

doi:10.1016/0304-3975(94)90156-2
fatcat:xk7qvvct25gkjkcvt3werskyya
*O*(log'*n*) such clusters, and we spend*amortized*constant*time*apiece, for a total update*time*of*O*(*log2**n*); all the other operations take*O*(logn)*time*. ... vertices*in**O*(log*n*)*time*. ...##
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Cache-conscious structure layout

1999
*
SIGPLAN notices
*

Hardware trends have produced an increasing disparity between processor speeds and memory access

doi:10.1145/301631.301633
fatcat:gzbvmob3frhpzkdp2k3rvo3bxm
*times*. ... tree reorganizer that utilizes topology information to cluster and color the structure. ccmalloc is a cache-conscious heap allocator that attempts to co-locate contemporaneously accessed data elements*in*... (c/2 x k x a + 1) (*log2*(*n*+ 1) -*log2*(c/2 x k x a + l))/(*log2*(k + 1)) ms = l%$" + 1) =*log2*(*n*+ 1) l%# + 1) Figure 9 . ...##
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Cache-conscious structure layout

1999
*
Proceedings of the ACM SIGPLAN 1999 conference on Programming language design and implementation - PLDI '99
*

Hardware trends have produced an increasing disparity between processor speeds and memory access

doi:10.1145/301618.301633
dblp:conf/pldi/ChilimbiHL99
fatcat:nop647je5ffibjp5fux3ugnjai
*times*. ... tree reorganizer that utilizes topology information to cluster and color the structure. ccmalloc is a cache-conscious heap allocator that attempts to co-locate contemporaneously accessed data elements*in*... (c/2 x k x a + 1) (*log2*(*n*+ 1) -*log2*(c/2 x k x a + l))/(*log2*(k + 1)) ms = l%$" + 1) =*log2*(*n*+ 1) l%# + 1) Figure 9 . ...##
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On the convex layers of a planar set

1985
*
IEEE Transactions on Information Theory
*

The algorithm runs

doi:10.1109/tit.1985.1057060
fatcat:yaon7b76g5g23mkufm2dusw3ky
*in**O*(*n*log*n*)*time*and requires*O*(*n*) space. ... Let S be a set of*n*points*in*the Euclidean plane. ... A number of*O*(n2)*time*algorithms for computing convex layers have been found [8], [17] , but the most efficient method previously known for this problem requires*O*(*n**log2**n*)*time*[13] . ...##
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Efficient parallel algorithms on restartable fail-stop processors

1991
*
Proceedings of the tenth annual ACM symposium on Principles of distributed computing - PODC '91
*

=

doi:10.1145/112600.112603
dblp:conf/podc/KanellakisS91
fatcat:cvyk3523cvhodgp7hh76uojpci
*N*) overhead ratio, and*O*(min{*N*+ Plog 2*N*+ M log*N*,*N*p 0 6 )) (sub-quadratic) completed work, where _f is the number of failures during this step's simulation. ... This strategy is work-optimal when the number of simulating processors is P < NI log 2*N*and the total number of failures per each simulated*N*processor step is*O*(*N*/ log*N*). ... without restarts: What is the worst We thank Jeff Vitter for helpful discussions, and Franico case completed work S, anld overhead ratio a of the Preparata for reviewing an earlier draft. algorithm X*in*...##
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Algorithm Engineering for Cut Problems
[article]

2021
*
arXiv
*
pre-print

All of these algorithms are efficient

arXiv:2108.04566v1
fatcat:4tpyybkhsvg6toiuxkvdvychqu
*in*practice and freely available for use. ...*In*this work, we aim to partition the vertices of a graph into multiple blocks while minimizing the number of edges that connect different blocks. ... Goranci et al. [79] manage to remove the dependence on λ from the update*time*and give an incremental algorithm with*O*log3*n*log*log2**n**amortized**time*per ...##
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Efficient detection of quasiperiodicities in strings

1993
*
Theoretical Computer Science
*

It is shown here that all maximal quasiperiodic substrings of a string Y of

doi:10.1016/0304-3975(93)90159-q
fatcat:urf6fuce7reatg7veey2ew3ypm
*n*symbols can be detected*in**time**O*(*n*log' II). ... A string z is quasiprriodic if there is a second string w#z such that the occurrences of I\'*in*2 cover I entirely, i.e., every position of z falls within some occurrence of w*in*z. ... computation will be*O*(*n**log2**n*). ...##
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Fully dynamic cycle-equivalence in graphs

*
Proceedings 35th Annual Symposium on Foundations of Computer Science
*

W e also present an algorithm for plane graphs with

doi:10.1109/sfcs.1994.365718
dblp:conf/focs/Henzinger94
fatcat:bq7fbnh2enhzxgb4ienmuvfo3e
*O*(1ogn) update and query*time*and for planar graphs with*O*(1ogn) insertion*time*and*O*(*log2**n*) que y and deletion*time*. ... I*n*an nnode graph OUT data structure executes an edge insertion OT deletion*in**O*(fi1ogn)*time*and answers the query whether two given edges are cycle-equivalent*in**O*(log2n)*time*. ...*Finding*the highest unmarked ancestor of a topology node takes*time**O*(1ogn). Thus, it takes*time**O*(*log2**n*) to*find*the highest unmarked ancestor for all topology nodes that represent x . ...##
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Mithril: Stake-based Threshold Multisignatures
[article]

2021
*
IACR Cryptology ePrint Archive
*

-as opposed to number of parties-and we are interested

dblp:journals/iacr/ChaidosK21
fatcat:t774dzuyuvdujgx3eqbz56kowa
*in*scalability, i.e., the complexity of critical operations depends only logarithmically*in*the number of participants (who are assumed to be numerous ... We formalize the primitive*in*the universal composition setting and propose efficient constructions for STMs. ... Furthermore, we know that h*log2*(*N*) = h*log2*(*N*) . Thus, there must exist a minimal k such that h k = h k but h k+1 = h k+1 . ...
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