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

Daniel Harabor and Adi Botea and Philip Kilby
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.  ... 
arXiv:1106.4083v1 fatcat:igz6hgy45vbpzmfwaezk7tpfsa

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

Christopher A. Cullenbine, R. Kevin Wood, Alexandra M. Newman
2013 Networks  
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

Richard R. Brooks
2009 International Journal of Distributed Sensor Networks  
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

Yuxuan Zhang, Ruizhe Zhang, Andrew C. Potter
2021 Quantum  
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]

Yuxuan Zhang, Ruizhe Zhang, Andrew C. Potter
2021 arXiv   pre-print
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

Masahiro Nakao, Maaki Sakai, Yoshiko Hanada, Hitoshi Murai, Mitsuhisa Sato
2021 Parallel Computing  
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

Alan A. Bertossi, Cristina M. Pinotti, Romeo Rizzi, Anil M. Shende
2004 Journal of Parallel and Distributed Computing  
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

Hans L. Bodlaender
1990 Information and Computation  
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

Witold Kazimierski, Agnieszka Sawczak, Natalia Wawrzyniak
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 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

Trong Viet Ho, Olivier Bonaventure, Yves Deville, Pham Quang Dung, Pierre Francois
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 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]

Shabbir Ahmed, Qie He, Shi Li, George Nemhauser
2016 arXiv   pre-print
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]

Assaf Hallak, Shie Mannor
2012 arXiv   pre-print
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]

Daniel Gottesman, Sandy Irani
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.  ... 
arXiv:0905.2419v2 fatcat:vlgd4ofus5h43dzpgvjapn5fgy

Comparison Theorems for Reversible Markov Chains

Persi Diaconis, Laurent Saloff-Coste
1993 The Annals of Applied Probability  
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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