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Solving problems on recursively constructed graphs

2008
*
ACM Computing Surveys
*

Fast algorithms can be created for many

doi:10.1145/1456650.1456654
fatcat:i4l5pratpzb35prq4df7ar3pka
*graph**problems*when instances are confined to classes of*graphs*that are*recursively**constructed*. ... that legitimize their identity as*recursively**constructed**graphs*. ...*Solving**Problems**on**Recursively**Constructed**Graphs*· 21 s A B C D E F H I J K A A B A E B E B B A B A B E E E C C D C H D H D D C D C D H H H E A B E F F I F J I J I H C D H I F I F I J J J J F I J K C ...##
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Using modular decomposition technique to solve the maximum clique problem
[article]

2017
*
arXiv
*
pre-print

Our algorithm takes the modular decomposition tree from the paper of Tedder et. al. and finds solution

arXiv:1710.04040v1
fatcat:6fd6kkf5yfctfittgmu57h22da
*recursively*. Also, we propose algorithms to*construct**graphs*with modules. ... In this article we use the modular decomposition technique for exact*solving*the weighted maximum clique*problem*. ... of MC*problem*and then*solve*it using some general algorithm for weighted maximum clique*problem*. ...##
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AN IMPROVED ALGORITHM FOR FINDING TREE DECOMPOSITIONS OF SMALL WIDTH

2000
*
International Journal of Foundations of Computer Science
*

A consequence is that the fundamental disjoint rooted paths

doi:10.1142/s0129054100000247
fatcat:gx5l67aqpfal3f7eixhcdttshu
*problem*can now be*solved*in O(n 2 ) time. This is the primary motivation for this paper. ... We present a modi cation of Bodlaender's linear time algorithm that, for constant k, determines whether an input*graph*G = (V; E) has treewidth k and, if so,*constructs*a tree decomposition of G of width ... Second, we have streamlined the*construction*of G (the*graph*the algorithm*recurses**on*) so the algorithm is simpler and the*graph*G is smaller. ...##
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Page 4309 of Mathematical Reviews Vol. , Issue 88h
[page]

1988
*
Mathematical Reviews
*

*Construction*of

*recursive*programs: Principles of

*construction*; Example 1. Draw- ing a figure within a figure; Example 2. Binary search; Example 3. Sorting by partitioning (‘quicksort’); Example 4. ...

*One*algorithm is a vectorized matrix-vector multiplication, and the other is a new, vectorized, overlapping-block iterative method for

*solving*finite element equations.” ...

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Algorithmic Meta-Theorems for Monotone Submodular Maximization
[article]

2018
*
arXiv
*
pre-print

We consider a monotone submodular maximization

arXiv:1807.04575v1
fatcat:ye2o43726zfyvfc7vijifqaptm
*problem*whose constraint is described by a logic formula*on*a*graph*. ... Formally, we prove the following three 'algorithmic metatheorems.' (1) If the constraint is specified by a monadic second-order logic*on*a*graph*of bounded treewidth, the*problem*is*solved*in n^O(1) time ... Acknowledgment We thank Antoine Amarilli for confirming the structuredness of their*construction*of DNNF in [1] . ...##
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Binary search and recursive graph problems

1997
*
Theoretical Computer Science
*

A

doi:10.1016/s0304-3975(96)00266-6
fatcat:dz3dkn7gevdjnflzulbl2z5rm4
*graph*G = (V, E) is*recursive*if every node of G has a finite number of neighbors, and both V and E are*recursive*(i.e., decidable). ... We examine the complexity of identifying the number of connected components of an infinite*recursive**graph*, and other related*problems*, both when an upper bound to that value is given a priori or not. ... We show that ]log(c + l)l queries is a tight bound*on*the number of queries necessary to*solve*the*problem*, even if a more powerful oracle is used. ...##
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An efficient programming model for memory-intensive recursive algorithms using parallel disks

2012
*
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation - ISSAC '12
*

We demonstrate the ideas

doi:10.1145/2442829.2442876
dblp:conf/issac/SlaviciKCL12
fatcat:iajugpkenzavphv72avrcavyim
*on*a largest computation of its kind: the determinization via subset*construction*and minimization of very large nondeterministic finite set automata (NFA). ... Research in this area over the past 10 years has focused*on*per-*problem*solutions, without providing much insight into the connection between legacy algorithms and out-of-core algorithms. ... This type of*recursion*corresponds to a callgraph in which a sub-*problem*can be*solved*by aggregating the results of n sub-sub-*problems*. ...##
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On the complexity of finding the chromatic number of a recursive graph II: the unbounded case

1989
*
Annals of Pure and Applied Logic
*

Most of our results are also true for highly

doi:10.1016/0168-0072(89)90037-7
fatcat:e6wj33qzebbwld2pv2refc2lhe
*recursive**graphs*(*graphs*where*one*can determine the neighbors of a given node*recursively*), though there are some interesting differences when queries to K ... A*recursive**graph*is a*graph*whose edge set and vertex set are both*recursive*. ... In this section we show that if f(n) queries suffice to*solve*the unbounded search*problem*, then f(n) queries can be used to find the chromatic number of a*recursive**graph*; and conversely that if d(n) ...##
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On energy optimized averaging in wireless sensor networks

2009
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Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference
*

This

doi:10.1109/cdc.2009.5400149
dblp:conf/cdc/PaschalidisL09
fatcat:prj5ibbitzaytahvvajk7hz6wy
*problem*has been shown to be NP-complete and can only be*solved*for small instances. We devise a semi-definite relaxation and establish bounds*on*the optimal cost. ... We also develop a series of*graph*-based algorithms that yield energy efficient bidirectional spanning trees and establish associated bounds*on*the optimal cost. ... •*Recursive*SDP from MILP • Relaxation • Sampling and Rounding , • The Framework of*Recursive*SDP Algorithm •Bounds Distributed*Graph*-Based Algorithms • Augmented*Graph**Construction*• ...##
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On Finding Subpaths With High Demand
[chapter]

2018
*
Operations Research Proceedings
*

We introduce a path-

doi:10.1007/978-3-319-89920-6_48
dblp:conf/or/SchwartzBB17
fatcat:wd73erplrzhsfnxu5fdwkqef5e
*graph*to prevent multiple generations of the same subpath and give a*recursive*approach to compute the demands of all subpaths. ... We study the*problem*of finding subpaths with high demand in a given network that is traversed by several users. ... If the subpath-*graph*is*constructed*, our*recursive*algorithm to*solve*the SLCP runs in O(s). ...##
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Optimality Program in Segment and String Graphs

2019
*
Algorithmica
*

best

doi:10.1007/s00453-019-00568-7
fatcat:y6rwhbhpdfhuzp4rhg65qx3z7e
*on*general*graphs*. ... Among our results, we show that, quite surprisingly, 3-Coloring can also be*solved*in time 2 O(n 2/3 log O(1) n)*on*string*graphs*while an algorithm running in time 2 o(n) for 4-Coloring even*on*axisparallel ... Theorem 10 For every fixed k 4, the k-Coloring*problem*of a 2-Dir*graph*cannot be*solved*in time 2 o(n) , unless the ETH fails. Proof We modify the*construction*from the proof of Theorem 9. ...##
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An efficient parallel algorithm for shortest paths in planar layered digraphs

2004
*
Journal of Zhejiang University: Science A
*

The algorithms uses a divide and conquer approach and is based

doi:10.1631/jzus.2004.0518
fatcat:ww7htm2e6ffinlwcs5kykjfndu
*on*the novel idea of a*one*-way separator, which has the property that any directed path can be crossed only once. ... This paper presents an efficient parallel algorithm for the shortest path*problem*in planar layered digraphs that runs in O(log 3 n) time with n processors. ... source and exactly*one*sink*recursively**constructed*by series and parallel compositions). ...##
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A comparative study on three graph-based constructive algorithms for multi-stage scheduling with blocking

2017
*
Journal of Industrial and Management Optimization
*

Based

doi:10.3934/jimo.2018040
fatcat:jkcbpl53hjbhbmvfyvze2cqfoa
*on*an alternative*graph*that is an extension of classical disjunctive*graph*, a new and generic polynomial-time algorithm is proposed to*construct*a feasible schedule with a given job processing sequence ... The comparison shows that the proposed algorithm has the following advantages: i) it is more adaptive because it can be applied to three different types of scheduling*problems*(i.e., permutation flow-shop ... The authors are very grateful to the editors and the anonymous reviewers for their*constructive*comments and suggestions that have led to an improved version of this paper. ...##
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Spanning Trees of Recursive Scale-Free Graphs
[article]

2022
*
arXiv
*
pre-print

We present a link-by-link rule-based method for

arXiv:2112.07325v2
fatcat:sfcshaqa5fcwdcpzslyts4mgky
*constructing*all members of the ensemble of spanning trees for any*recursively*generated, finitely articulated*graph*, such as the DGM net. ... .), and thus provides solutions to several optimization*problems*. The analysis of spanning trees enhances the usefulness of*recursive**graphs*as sophisticated models for everyday life complex networks. ... While finding this number is, in general, an intractable*problem*, we hope that the*recursive*properties of these*graphs*might provide a convenient foothold for such a*problem*. ...##
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Solving SDD linear systems in nearlymlog1/2ntime

2014
*
Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14
*

Our approach follows the

doi:10.1145/2591796.2591833
dblp:conf/stoc/CohenKMPPRX14
fatcat:uj5ipnfeerhbjinf55wkhmgbgu
*recursive*preconditioning framework, which aims to reduce*graphs*to trees using iterative methods. ... Both of these components are used in a variety of other algorithms, and our approach also extends to the dual*problem*of computing electrical flows. ...*Recursive*preconditioning that reduces a*solve*to several*ones**on*smaller, but similar*graphs*. 2. Ultra-sparsifiers that lead to such smaller*graphs*. 3 . ...
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