A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
On constructing snakes in powers of complete graphs

1998
*
Discrete Mathematics
*

chords)

doi:10.1016/s0012-365x(97)00039-3
fatcat:z6skf5clfbdqdmmbfyjz5aclyu
*in*the cartesian product K~*of*d copies*of*the*complete**graph*Kin. ... We prove the conjecture*of*Abbott and Katchalski that for every m ~> 2 there is a positive constant 2,. such that S(K~n ) >~ 2mnd-lS(Ka~ -1) where S(Ka~) is the length*of*the longest*snake*(cycle without ... Hence, by Lemma 2.2(ii), (rg [] 9) [] 7n = cg [] 7n q is a*snake**in*Gp+q, and the proof is*complete*. []3.*Construction**of*long snakesAssume that d >~4. ...##
###
Further results on snakes in powers of complete graphs

1991
*
Discrete Mathematics
*

Katchalski, Further results

doi:10.1016/0012-365x(91)90103-9
fatcat:2snziye2sfgbhppvo4ts3zgy6e
*on**snakes**in**powers**of**complete**graphs*, Discrete Mathematics 91 (1991) 111-120. ... Introduction By a*snake**in*a finite*graph*G is meant a simple cycle without chords. We denote by S(G) the length*of*a longest*snake**in*G. ... Let K,, denote the*complete**graph*with n vertices and let K," denote the product*of*d copies*of*K,,. ...##
###
The Minimum Shared Edges Problem on Grid-like Graphs
[article]

2017
*
arXiv
*
pre-print

We study the NP-hard Minimum Shared Edges (MSE) problem

arXiv:1703.02332v2
fatcat:hdipsn4xdjbyjhl26bmowo2agy
*on**graphs*: decide whether it is possible to route p paths from a start vertex to a target vertex*in*a given*graph*while using at most k edges more ... We show that MSE can be decided*on*bounded (i.e. finite) grids*in*linear time when both dimensions are either small or large compared to the number p*of*paths. ... This is possible since the number*of*vertices*in*G is a*power**of*two. ...##
###
The Minimum Shared Edges Problem on Grid-Like Graphs
[chapter]

2017
*
Lecture Notes in Computer Science
*

We study the NP-hard Minimum Shared Edges (MSE) problem

doi:10.1007/978-3-319-68705-6_19
fatcat:ia7r2s2zy5gtla342gxsyehqr4
*on**graphs*: decide whether it is possible to route p paths from a start vertex to a target vertex*in*a given*graph*while using at most k edges more ... We show that MSE can be decided*on*bounded grids*in*linear time when both dimensions are either small or large compared to the number p*of*paths. ... This is possible since the number*of*vertices*in*G is a*power**of*two. ...##
###
Finding Longest Paths in Hypercubes: 11 New Lower Bounds for Snakes, Coils, and Symmetrical Coils
[chapter]

2015
*
Lecture Notes in Computer Science
*

INDEX WORDS: stochastic beam search;

doi:10.1007/978-3-319-19066-2_3
fatcat:2igyr5l5ovb6nh4ch3vjg3p4by
*snake*-*in*-the-box; combinatorial optimization;*graph*search; hypercube; heuristic search FINDING LONGEST PATHS*IN*HYPERCUBES: 11 NEW LOWER BOUNDS FOR*SNAKES*, COILS, ... Stochastic Beam Search, a non-deterministic variant*of*Beam Search, provides the overall structure for our search, while*graph*theory based techniques are used*in*the computation*of*a generational fitness ... ACKNOWLEDGMENTS We thank Dustin Cline and Thomas Horton for their important contributions to this project,*Snake*-*in*-the-Box research, and the Institute for Artificial Intelligence. ...##
###
Page 7184 of Mathematical Reviews Vol. , Issue 95m
[page]

1995
*
Mathematical Reviews
*

A

*snake**in*a*graph*is a cycle without chords. Denote by S(K/) the length*of*a longest*snake**in*the product*of*d copies*of*the*complete**graph**on*n vertices. ... Abbott (3-AB; Edmonton, AB) 95m:05149 05C38 05C35 Wojciechowski, Jerzy (1-WV; Morgantown, WV) Long*snakes**in**powers**of*the*complete**graph*with an odd number*of*vertices. (English summary) J. ...##
###
New Bounds for the Snake-in-the-Box Problem
[article]

2016
*
arXiv
*
pre-print

The

arXiv:1603.05119v2
fatcat:dmlvnhuhazbr3efjiyhscntr3q
*Snake*-*in*-the-Box problem is that*of*finding a longest induced path*in*an n-dimensional hypercube. We prove new lower bounds for the values n∈{11,12,13}. ... The Coil-*in*-the-Box problem is that*of*finding a longest induced cycle*in*an n-dimensional hypercube. We prove new lower bounds for the values n∈{12,13}. ... Acknowledgements This work made use*of*the facilities*of*the Hamilton HPC Service*of*Durham University. ...##
###
Page 5549 of Mathematical Reviews Vol. , Issue 95i
[page]

1995
*
Mathematical Reviews
*

Here a(H) is the maximum size

*of*a*snake*containing no edge*of*H. This is analogous to the maximum size*of*a stable set*in*a random*graph*. ... We take £(H) to be the minimum number*of*edges*of*H contained*in*any n-*snake*. ...##
###
The Snake Optimizer for Learning Quantum Processor Control Parameters
[article]

2020
*
arXiv
*
pre-print

*In*this whitepaper, we introduce the

*Snake*Optimizer for efficiently and quickly solving such optimization problems by leveraging concepts

*in*artificial intelligence, dynamic programming, and

*graph*optimization ... This application enabled state-

*of*-the-art system performance

*on*a 53 qubit quantum processor, serving as a key component

*of*demonstrating quantum supremacy. ... CONTRIBUTIONS P.V.K. conceived the

*Snake*Optimizer. P.V.K and J.K. developed ideas for calibration stack integration. J.M.M. and H.N. supported research and development. V. ...

##
###
The firefighter problem for graphs of maximum degree three

2007
*
Discrete Mathematics
*

We show that the firefighter problem is NP-

doi:10.1016/j.disc.2005.12.053
fatcat:ncprza34kjhbjinrcw33nf4jaa
*complete*for trees*of*maximum degree three, but*in*P for*graphs**of*maximum degree three if the fire breaks out at a vertex*of*degree at most two. ... These lead to bounds*on*the maximum number*of*vertices that can be saved. NP-*completeness**of*the firefighter problem*on*bipartite*graphs*is established*in*[10] . ...*In*the*construction**of*(T , r), these two clauses gave rise to 12*snake*trees: Claim 2. ...##
###
Lengths of snakes in boxes

1967
*
Journal of Combinatorial Theory
*

A

doi:10.1016/s0021-9800(67)80026-7
fatcat:3hslhftornhr5n25x5alljqz3a
*snake**in*a*graph*G is a simple circuit C*in*G such that C has no chords*in*G--that is, every edge*of*G which joins two vertices*of*C is*in*fact an edge*of*C. ... For each d ~ 2 let S(d) denote the length (number*of*vertices)*of*the longest*snake**in*the*graph*I a formed by the vertices and edges*of*the d-dimensional cube. ... Then*one**of*the*graphs*P C~ I s and P c5 1, 8 has at least five vertices and thus is as*in**one**of*the last two diagrams above. ...##
###
Page 23 of Mathematical Reviews Vol. 55, Issue 1
[page]

1978
*
Mathematical Reviews
*

*Snakes*

*in*

*powers*

*of*

*complete*

*graphs*. SIAM J. Appl. Math. 32 (1977), no. 2, 347-355. ...

*In*this paper, some

*snakes*are

*constructed*for the class

*of*

*graphs*K,° (product

*of*d copies

*of*the

*complete*

*graph*K,) and thus some lower bounds for the length

*of*the longest

*snakes*are obtained. ...

##
###
Long Snakes in Powers of the Complete Graph with an Odd Number of Vertices

1994
*
Journal of the London Mathematical Society
*

*In*[5] Abbott and Katchalski ask if there exists a constant c > 0 such that for every d ≥ 2 there is a

*snake*(cycle without chords)

*of*length at least c3 d

*in*the product

*of*d copies

*of*the

*complete*

*graph*... product

*of*d copies

*of*the

*complete*

*graph*K n . ... Hence by Property 2 (ii ), γ n ⊗ (D ⊗ C) is a

*snake*

*in*K n × K d n × H = K d+1 n × H, and the proof is

*complete*.

*Construction*

*of*Well Distributed Chains Let C be a chain

*of*paths

*in*a

*graph*G. ...

##
###
Snake graph calculus and cluster algebras from surfaces III: Band graphs and snake rings
[article]

2015
*
arXiv
*
pre-print

The definition

arXiv:1506.01742v2
fatcat:huq4k3mrjja2ra5wndavllnch4
*of*the rings requires the*snake**graph*calculus which is*completed**in*this paper building*on*two earlier articles*on*the subject. ...*One**of*the main results*of*the current paper is the*completion**of*the explicit*construction**of*these bijections. ... The*construction**of*abstract*snake**graphs*and band*graphs*is*completely*detached from triangulated surfaces. Our goal is to study these objects*in*a combinatorial way. ...##
###
The Parameterized Complexity of Motion Planning for Snake-Like Robots
[article]

2019
*
arXiv
*
pre-print

Unfortunately, already

arXiv:1903.02445v1
fatcat:epne2dsumvhjhgzc5xnpqywdoa
*on*grid*graphs*, this problem is PSPACE-*complete*[Biasi and Ophelders, 2016]. ... Nevertheless, we prove that even*on*general*graphs*, the problem is solvable*in*time k^O(k)|I|^O(1) where k is the size*of*the*snake*, and |I| is the input size. ... Roughly speaking, given t instances*of*Hamiltonian Cycle*on*grid*graphs*, our*construction**of*an instance*of**Snake*Game is as follows. ...
« Previous

*Showing results 1 — 15 out of 7,838 results*