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Symmetry-Based Search Space Reduction For Grid Maps
[article]
2011
arXiv
pre-print
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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. ...
arXiv:1106.4083v1
fatcat:igz6hgy45vbpzmfwaezk7tpfsa
Page 4448 of Mathematical Reviews Vol. , Issue 84k
[page]
1984
Mathematical Reviews
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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
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This problem, with intelligence-gathering and war-fighting applications, seeks a minimum-weight, minimal s-t cut E C ⊆ E 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] ). ...
doi:10.1002/net.21514
fatcat:gmabxdmfj5hbje56uiuk5ox2de
Sensor Network Self-Organization Using Random Graphs
2009
International Journal of Distributed Sensor Networks
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Applications 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. ...
doi:10.1080/15501320802498307
fatcat:io4pvsiqxnhnracmx5pw6tfnf4
QED driven QAOA for network-flow optimization
2021
Quantum
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This results 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 . ...
doi:10.22331/q-2021-07-27-510
fatcat:7fh3pxhzmjdjjalvzg5dvslnke
QED driven QAOA for network-flow optimization
[article]
2021
arXiv
pre-print
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This results 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 . ...
arXiv:2006.09418v3
fatcat:ktjqvqao6zb3dfjxr42vu23ucq
Graph optimization algorithm for low-latency interconnection networks
2021
Parallel Computing
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Such network topologies can be defined as the order/degree problem 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. ...
doi:10.1016/j.parco.2021.102805
fatcat:5bu67l3yirg2xmkveodtakq5o4
Channel assignment for interference avoidance in honeycomb wireless networks
2004
Journal of Parallel and Distributed Computing
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On a flat region without geographical barriers and with 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. ...
doi:10.1016/j.jpdc.2004.06.006
fatcat:uuh7cdl6r5hjjfidnj4c3uhvsq
The complexity of finding uniform emulations on paths and ring networks
1990
Information and Computation
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This can be done 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 +. ...
doi:10.1016/0890-5401(90)90027-f
fatcat:5wqczfhujje23dgyszfgqihsye
Analysis of Graph Searching Algorithms for Route Planning in Inland Navigation
2015
TransNav: International Journal on Marine Navigation and Safety of Sea Transportation
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Route planning is one of the core functionalities of modern navigational systems also 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. ...
doi:10.12716/1001.09.02.17
fatcat:53opcggwxvgujo7gketyu4cnxe
Using local search for traffic engineering in switched Ethernet networks
2010
2010 22nd International Teletraffic Congress (lTC 22)
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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 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. ...
doi:10.1109/itc.2010.5608731
dblp:conf/teletraffic/VietBDDF10
fatcat:gre5jphkhjc27essoixm5soyuq
On the computational complexity of minimum-concave-cost flow in a two-dimensional grid
[article]
2016
arXiv
pre-print
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We study the minimum-concave-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. ...
arXiv:1602.08515v1
fatcat:wixoo6ahbvgyfd66455oqtytjy
How to sample if you must: on optimal functional sampling
[article]
2012
arXiv
pre-print
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Although this problem is 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. ...
arXiv:1208.2417v1
fatcat:3puop5b65vfrlctu5gwjxsa75u
The Quantum and Classical Complexity of Translationally Invariant Tiling and Hamiltonian Problems
[article]
2010
arXiv
pre-print
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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. ...
arXiv:0905.2419v2
fatcat:vlgd4ofus5h43dzpgvjapn5fgy
Comparison Theorems for Reversible Markov Chains
1993
The Annals of Applied Probability
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We introduce geometric comparison inequalities that give bounds on the eigenvalues of a reversible Markov chain 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. ...
doi:10.1214/aoap/1177005359
fatcat:fej67r75dnbbvpqvtkler4hy44
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