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Symmetry-Based Search Space Reduction For Grid Maps
[article]

2011
*
arXiv
*
pre-print

*In*this paper we explore a

*symmetry*-based search space reduction technique which can speed up optimal pathfinding on

*undirected*

*uniform*-

*cost*

*grid*maps by up to 38 times. ... Our algorithm is fast, memory efficient and retains the same optimality and completeness guarantees as searching on an unmodified

*grid*map. ... We also thank Ariel Felner and Meir Goldenberg for providing us with assistance

*in*comparing RSR with their enhanced Portal Heuristic algorithm. ...

##
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Page 4448 of Mathematical Reviews Vol. , Issue 84k
[page]

1984
*
Mathematical Reviews
*

The third set of results relate the difficulty of deciding the

*cost*of playing a pebble game on a given input graph G to the bandwidth of G.” Frank, Andras Disjoint*paths**in*a rectilinear*grid*. ...*paths*between these pairs of vertices. ...##
###
Theoretical and computational advances for network diversion

2013
*
Networks
*

This problem, with intelligence-gathering and war-fighting applications, seeks a minimum-weight, minimal s-t cut E C ⊆ E

doi:10.1002/net.21514
fatcat:gmabxdmfj5hbje56uiuk5ox2de
*in*G such that e ∈ E C . ... The network-diversion problem (ND) is defined on a directed or*undirected*graph G = (V , E ) having nonnegative edge weights, a source vertex s, a sink vertex t , and a "diversion edge" e . ... The*path*-penalty term may be viewed as a*symmetry*-breaking device (e.g., Sherali and Smith [39] ). ...##
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Sensor Network Self-Organization Using Random Graphs

2009
*
International Journal of Distributed Sensor Networks
*

Applications

doi:10.1080/15501320802498307
fatcat:io4pvsiqxnhnracmx5pw6tfnf4
*in*system security and surveillance networks are given. ... Sensor networks are deployed*in*, and react with, chaotic environments. Self-organizing peer-to-peer networks have admirable survivability characteristics. ... By definition, the graph is*in*its supercritical phase. By*symmetry*, when P (2) < P the likelihood that a*path*of j hops connects any two nodes decreases monotonically with j. ...##
###
QED driven QAOA for network-flow optimization

2021
*
Quantum
*

This results

doi:10.22331/q-2021-07-27-510
fatcat:7fh3pxhzmjdjjalvzg5dvslnke
*in*an exponential reduction*in*the size of the configuration space that needs to be explored, which we show through numerical simulations, yields higher quality approximate solutions compared ... We outline a specific implementation for edge-disjoint*path*(EDP) problems related to traffic congestion minimization, numerically analyze the effect of initial state choice, and explore trade-offs between ... each edge from the*uniform*distribution on the unit interval [0, 1], and seeding the state-preparation step with a uniformlyrandomly chosen*path*, |P 0 . ...##
###
QED driven QAOA for network-flow optimization
[article]

2021
*
arXiv
*
pre-print

This results

arXiv:2006.09418v3
fatcat:ktjqvqao6zb3dfjxr42vu23ucq
*in*an exponential reduction*in*the size of the configuration space that needs to be explored, which we show through numerical simulations, yields higher quality approximate solutions compared ... We outline a specific implementation for edge-disjoint*path*(EDP) problems related to traffic congestion minimization, numerically analyze the effect of initial state choice, and explore trade-offs between ... each edge from the*uniform*distribution on the unit interval [0, 1], and seeding the state-preparation step with a uniformlyrandomly chosen*path*, |P 0 . ...##
###
Graph optimization algorithm for low-latency interconnection networks

2021
*
Parallel Computing
*

Such network topologies can be defined as the order/degree problem

doi:10.1016/j.parco.2021.102805
fatcat:5bu67l3yirg2xmkveodtakq5o4
*in*graph theory by modeling a network topology as an*undirected*graph. ... and average shortest*path*length (ASPL). ... Acknowledgment This research used the Cygnus system provided by Interdisciplinary Computational Science Program*in*the Center for Computational Sciences, University of Tsukuba. ...##
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Channel assignment for interference avoidance in honeycomb wireless networks

2004
*
Journal of Parallel and Distributed Computing
*

On a flat region without geographical barriers and with

doi:10.1016/j.jpdc.2004.06.006
fatcat:uuh7cdl6r5hjjfidnj4c3uhvsq
*uniform*traffic load, the network base stations are usually placed according to a regular plane tessellation, while the channels are permanently ... Under these assumptions, the CAP problem on honeycomb*grids*can be modeled as a suitable coloring problem. ... Two different tessellations may arise depending on the*symmetry*of the diamond, but*in*both cases each*grid*vertex can color itself*in*constant time. ...##
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The complexity of finding uniform emulations on paths and ring networks

1990
*
Information and Computation
*

This can be done

doi:10.1016/0890-5401(90)90027-f
fatcat:5wqczfhujje23dgyszfgqihsye
*in*time O(n). Step 1*costs*O(nc) time, step 2*costs*0(l), and step 3*costs*0(,'+ ') time. For each active region r, steps 4-7 are performed at most once. ... The following problem is NP-complete : [*UNIFORM*EMULATION ON A*PATH*for binary trees] Instance: An*undirected*, connected gruph G, which is a binary tree, and u positive integer n E N +. ...##
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Analysis of Graph Searching Algorithms for Route Planning in Inland Navigation

2015
*
TransNav: International Journal on Marine Navigation and Safety of Sea Transportation
*

Route planning is one of the core functionalities of modern navigational systems also

doi:10.12716/1001.09.02.17
fatcat:53opcggwxvgujo7gketyu4cnxe
*in*inland waters. ... The ubiquitous*undirected**uniform*-*cost**grid*map is a highly popular method for representing pathfinding environments*in*many fields, like video games or robotics (Harabor and Grastien, 2011) . ... Then by determining the size of a regular quadratic mesh (*grid*) and by overlapping map with it, an*undirected*graph can be built. ...##
###
Using local search for traffic engineering in switched Ethernet networks

2010
*
2010 22nd International Teletraffic Congress (lTC 22)
*

Congestion is usually handled by deploying more switches and installing higher bandwidth link bundles, although a better use of the existing infrastructure would allow to deal with congestion at lower

doi:10.1109/itc.2010.5608731
dblp:conf/teletraffic/VietBDDF10
fatcat:gre5jphkhjc27essoixm5soyuq
*cost*... Large switched Ethernet networks are deployed*in*campus networks, data centers and metropolitan area networks to support various types of services. ... -*Cost*:*Cost*of the least-*cost**path*to the root from the transmitting switch. ...##
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On the computational complexity of minimum-concave-cost flow in a two-dimensional grid
[article]

2016
*
arXiv
*
pre-print

We study the minimum-concave-

arXiv:1602.08515v1
fatcat:wixoo6ahbvgyfd66455oqtytjy
*cost*flow problem on a two-dimensional*grid*. ... The concave*cost*over each arc is assumed to be evaluated through an oracle machine, i.e., the oracle machine returns the*cost*over an arc*in*a single computational step, given the flow value and the arc ... Then there is an*undirected**path*between v 1,i and v 1,i*in*T f,1 and an*undirected**path*between v 1,j and v 1,j*in*T f,2 . These two*paths*cannot be vertex-disjoint by Lemma 2.6. ...##
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How to sample if you must: on optimal functional sampling
[article]

2012
*
arXiv
*
pre-print

Although this problem is

arXiv:1208.2417v1
fatcat:3puop5b65vfrlctu5gwjxsa75u
*in*the heart of the field of optimal design, no efficient solutions for the case with many functionals exist. ... We analyze sampling of a multivariate normal distribution with an unknown expectation that needs to be estimated:*in*our setup it is possible to sample the distribution from a given set of linear functionals ...*In*Figure 5 .2 (B) we compare our relaxed solution against the*uniform*distribution for the*grid*graph. ...##
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The Quantum and Classical Complexity of Translationally Invariant Tiling and Hamiltonian Problems
[article]

2010
*
arXiv
*
pre-print

*In*this paper, we show hardness of a classical tiling problem on an N x N 2-dimensional

*grid*and a quantum problem involving finding the ground state energy of a 1-dimensional quantum system of N particles ... Thus, an algorithm for these problems which runs

*in*time polynomial

*in*N (exponential

*in*the input size) would imply that EXP = NEXP or BQEXP = QMA_EXP, respectively. ... S.I. was supported

*in*part by NSF Grant CCR-0514082. Part of this work was done while both authors were visiting the Institute for Quantum Information at Caltech. ...

##
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Comparison Theorems for Reversible Markov Chains

1993
*
The Annals of Applied Probability
*

We introduce geometric comparison inequalities that give bounds on the eigenvalues of a reversible Markov chain

doi:10.1214/aoap/1177005359
fatcat:fej67r75dnbbvpqvtkler4hy44
*in*terms of the eigenvalues of a second chain. ... For this set of*paths*, we find EXAMPLE Let 27, be an 1 x m*grid**in*Z2 with lm n. ... Consider a*grid**in*Zd with size 1 , x x Zd = n and set 1 = max Zi. Fix*paths*on this*grid*by always moving first along the first axis, then along the second axis, etc. ...
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