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

Jacob Holm, Eva Rotenberg, Mikkel Thorup
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
We support updates 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  ... 
doi:10.1137/1.9781611975031.3 dblp:conf/soda/HolmRT18 fatcat:7i7ehjmdzjdxbm26tzy72rfe5q

Persistence, Amortization and Randomization

Paul F. Dietz, Rajeev Raman
1991 ACM-SIAM Symposium on Discrete Algorithms  
We show how to make some new data structures, including disjoint-set union-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.  ... 
dblp:conf/soda/DietzR91 fatcat:f5a4pr63tzgqrivh7fu7ql3fiu

Dynamic Planar Point Location in External Memory

J. Ian Munro, Yakov Nekrich, Michael Wagner
2019 International Symposium on Computational Geometry  
Our data structure supports queries 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 [  ... 
doi:10.4230/lipics.socg.2019.52 dblp:conf/compgeom/MunroN19 fatcat:ro5wyylxyjgxtcqef5dz5fx4b4

DYNAMIZATION OF THE TRAPEZOID METHOD FOR PLANAR POINT LOCATION IN MONOTONE SUBDIVISIONS

YI-JEN CHIANG, ROBERTO TAMASSIA
1992 International journal of computational geometry and applications  
Let 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  ... 
doi:10.1142/s0218195992000184 fatcat:utnmrf2nvfaqtlk5mej7xfq6k4

Parallel Tree Contraction Part 2: Further Applications

Gary L. Miller, John H. Reif
1991 SIAM journal on computing (Print)  
To see that the above algorithm works 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.  ... 
doi:10.1137/0220070 fatcat:i7bjji4aefes5ayetgrt2ywdfq

Consecutive interval query and dynamic programming on intervals

Alok Aggarwal, Takeshi Tokuyama
1998 Discrete Applied Mathematics  
Given a set of 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.  ... 
doi:10.1016/s0166-218x(98)00021-3 fatcat:4pfauas4wzfqhknfrfxm55khdu

Data structures for two-edge connectivity in planar graphs

John Hershberger, Monika Rauch, Subhash Suri
1994 Theoretical Computer Science  
There are 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.  ... 
doi:10.1016/0304-3975(94)90156-2 fatcat:xk7qvvct25gkjkcvt3werskyya

Cache-conscious structure layout

Trishul M. Chilimbi, Mark D. Hill, James R. Larus
1999 SIGPLAN notices  
Hardware trends have produced an increasing disparity between processor speeds and memory access 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 .  ... 
doi:10.1145/301631.301633 fatcat:gzbvmob3frhpzkdp2k3rvo3bxm

Cache-conscious structure layout

Trishul M. Chilimbi, Mark D. Hill, James R. Larus
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 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 .  ... 
doi:10.1145/301618.301633 dblp:conf/pldi/ChilimbiHL99 fatcat:nop647je5ffibjp5fux3ugnjai

On the convex layers of a planar set

B. Chazelle
1985 IEEE Transactions on Information Theory  
The algorithm runs 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] .  ... 
doi:10.1109/tit.1985.1057060 fatcat:yaon7b76g5g23mkufm2dusw3ky

Efficient parallel algorithms on restartable fail-stop processors

Paris C. Kanellakis, Alex A. Shvartsman
1991 Proceedings of the tenth annual ACM symposium on Principles of distributed computing - PODC '91  
= 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  ... 
doi:10.1145/112600.112603 dblp:conf/podc/KanellakisS91 fatcat:cvyk3523cvhodgp7hh76uojpci

Algorithm Engineering for Cut Problems [article]

Alexander Noe
2021 arXiv   pre-print
All of these algorithms are efficient 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  ... 
arXiv:2108.04566v1 fatcat:4tpyybkhsvg6toiuxkvdvychqu

Efficient detection of quasiperiodicities in strings

Alberto Apostolico, Andrzej Ehrenfeucht
1993 Theoretical Computer Science  
It is shown here that all maximal quasiperiodic substrings of a string Y of 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).  ... 
doi:10.1016/0304-3975(93)90159-q fatcat:urf6fuce7reatg7veey2ew3ypm

Fully dynamic cycle-equivalence in graphs

M.R. Henzinger
Proceedings 35th Annual Symposium on Foundations of Computer Science  
W e also present an algorithm for plane graphs with 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 .  ... 
doi:10.1109/sfcs.1994.365718 dblp:conf/focs/Henzinger94 fatcat:bq7fbnh2enhzxgb4ienmuvfo3e

Mithril: Stake-based Threshold Multisignatures [article]

Pyrros Chaidos, Aggelos Kiayias
2021 IACR Cryptology ePrint Archive  
-as opposed to number of parties-and we are interested 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 .  ... 
dblp:journals/iacr/ChaidosK21 fatcat:t774dzuyuvdujgx3eqbz56kowa
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