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Undirected edge geography

Aviezri S Fraenkel, Edward R Scheinerman, Daniel Ullman
1993 Theoretical Computer Science  
Ullman, Undirected edge geography, Theoretical Computer Science 112 (1993) 371-381.  ...  The game of edge geography is played by two players who alternately move a token on a graph from one vertex to an adjacent vertex, erasing the edge in between.  ...  and edge geography.  ... 
doi:10.1016/0304-3975(93)90026-p fatcat:of3bbev2nbdutadcckwvwpod5u

Evaluation of computer network security using attack undirected geography

Chanintorn Jittawiriyanukoon
2019 Indonesian Journal of Electrical Engineering and Computer Science  
Network security model based on attack undirected geography (AUG) is familiarized. First, analysis based upon association rules is presented then the attack threshold value is set from AUG.  ...  Geography is a necessary construct in computer networks.  ...  If all edges are undirected, or bi-directional, then the computer network is called an undirected network (geography).  ... 
doi:10.11591/ijeecs.v16.i3.pp1508-1514 fatcat:6wz5fr6w25c7terevnsl3trity

On the Complexity of the Misère Version of Three Games Played on Graphs [article]

Gabriel Renault, Simon Schmidt
2015 arXiv   pre-print
on both directed and undirected graphs.  ...  We investigate the complexity of finding a winning strategy for the misère version of three games played on graphs : two variants of the game NimG, introduced by Stockmann in 2004 and the game Vertex Geography  ...  Finding the misère outcome of an Edge Geography position on an undirected graph is pspace-complete. Proof. We reduce the problem from normal Edge Geography on undirected graphs.  ... 
arXiv:1401.0400v2 fatcat:fkmtni6u6vf47oyl4bltnvrvnq

On the complexity of the misère version of three games played on graphs

Gabriel Renault, Simon Schmidt
2015 Theoretical Computer Science  
on both directed and undirected graphs.  ...  We investigate the complexity of finding a winning strategy for the misère version of three games played on graphs: two variants of the game NimG, introduced by Stockmann in 2004 and the game Vertex Geography  ...  Finding the misère outcome of an Edge Geography position on an undirected graph is pspace-complete. Proof. We reduce the problem from normal Edge Geography on undirected graphs.  ... 
doi:10.1016/j.tcs.2015.06.034 fatcat:gzpbiqjo7bgn5ioqfit73zkiam

Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players

Jeffrey Bosboom, Charlotte Chen, Lily Chung, Spencer Compton, Michael Coulombe, Erik D. Demaine, Martin L. Demaine, Ivan Tadeu Ferreira Antunes Filho, Dylan Hendrickson, Adam Hesterberg, Calvin Hsu, William Hu (+3 others)
2020 Journal of Information Processing  
., 1 × n edge matching.  ...  planar 3-regular directed Hamiltonicity; we provide linear-time algorithms to find antidirected and forbidden-transition Eulerian paths; and we characterize the complexity of new partizan variants of the Geography  ...  Graph Partizan Geography Complexity undirected vertex vertex polynomial undirected vertex edge polynomial undirected edge vertex PSPACE-complete undirected edge edge PSPACE-complete  ... 
doi:10.2197/ipsjjip.28.987 fatcat:dltiyh2xofaxjpeytp7nyi6pam

Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players [article]

Jeffrey Bosboom, Charlotte Chen, Lily Chung, Spencer Compton, Michael Coulombe, Erik D. Demaine, Martin L. Demaine, Ivan Tadeu Ferreira Antunes Filho, Dylan Hendrickson, Adam Hesterberg, Calvin Hsu, William Hu (+3 others)
2020 arXiv   pre-print
., 1 × n edge matching.  ...  We analyze the computational complexity of several new variants of edge-matching puzzles.  ...  in/outdegree 2. • Undirected vertex-partizan vertex geography and undirected vertex-partizan edge geography can be solved in polynomial time. → Figure 18 : A gadget simulating a directed edge with undirected  ... 
arXiv:2002.03887v2 fatcat:fdclet2ygzg2tdcirqxpxwrn64

On the shortest path game: extended version [article]

Andreas Darmann and Ulrich Pferschy and Joachim Schauer
2015 arXiv   pre-print
The latter result is a surprising deviation from the complexity status of the closely related game Geography.  ...  The two players take turns in deciding in each vertex which edge to traverse next. The decider in each vertex also has to pay the cost of the chosen edge.  ...  [10] it was proved that also the undirected variant of Geography is PSPACE-complete.  ... 
arXiv:1506.00462v1 fatcat:dfdj7k3wmnfcnfxcdb7zy3hqbe

Complexity of path-forming games

Hans L. Bodlaender
1993 Theoretical Computer Science  
We will allow for parallel edges and self-loops in the undirected graphs that we are dealing with.  ...  EDGE GENERALIZED GEOGRAPHY can be solved in C(n) time on cacti.  ... 
doi:10.1016/0304-3975(93)90357-y fatcat:j5dhcbm4izcpzpvxfhz5nf2wza

Nimber-Preserving Reductions and Homomorphic Sprague-Grundy Game Encodings [article]

Kyle Burke, Matthew Ferland, Shanghua Teng
2022 arXiv   pre-print
We prove that Generalized Geography is complete for the natural class, I^P , of polynomially-short impartial rulesets under nimber-preserving reductions, a property we refer to as Sprague-Grundy-complete  ...  Edge-Geography and its undirected sub-family, Undirected Edge-Geography are both PSPACE-complete. The following proof sketch shows that Edge-Geography remains Sprague-Grundy complete. Proof.  ...  To fix this, we can simply have v b go to v a1 and v a2 which both only have a single edge to v s . It remains open whether Undirected Edge-Geography is Sprague-Grundy complete.  ... 
arXiv:2109.05622v2 fatcat:ksi27dd56bamnjjajoazestvhu

On the Shortest Path Game

Andreas Darmann, Ulrich Pferschy, Joachim Schauer
2017 Discrete Applied Mathematics  
The latter result is a surprising deviation from the complexity status of the closely related game Geography.  ...  The two players take turns in deciding in each vertex which edge to traverse next. The decider in each vertex also has to pay the cost of the chosen edge.  ...  [9] it was proved that also the undirected variant of Geography is PSPACE-complete.  ... 
doi:10.1016/j.dam.2015.08.003 fatcat:snjg6rjlsvesvmwtlxxhkjzgge

Feedback game on Eulerian graphs [article]

Naoki Matsumoto, Atsuki Nagao
2020 arXiv   pre-print
In this paper, we introduce a two-player impartial game on graphs, called a feedback game, which is a variant of the generalized geography. We study the feedback game on Eulerian graphs.  ...  Complexity of the feedback game Because the feedback game can be seen as a variant of the undirected edge geography, it is a simple idea to construct a reduction from the undirected edge geography to the  ...  Moreover, several variants of the generalized geography have been considered, e.g., the planar generalized geography [14] , edge geography [15] and undirected geography [11] .  ... 
arXiv:2002.09570v1 fatcat:iudbfcjy2bdjbnnmfqfhgp6bce

A PSPACE-complete Graph Nim [article]

Kyle Burke, Olivia George
2014 arXiv   pre-print
The games created by the reduction share strong similarities with Undirected (Vertex) Geography and regular Nim, both of which are in P.  ...  By reducing from Geography, we show that this game is PSPACE-hard.  ...  Figure 1 : 1 Our main gadget: reduce each directed edge from y to z to the undirected weighted graph shown here.  ... 
arXiv:1101.1507v3 fatcat:orrlwnu7h5bo5auidwieyjbgqq

Page 286 of Geographical Analysis Vol. 10, Issue 3 [page]

1978 Geographical Analysis  
Evans Let G=(V,E) be an undirected graph with weighted edges w(e,), jE E. A spanning tree T is a circuitless subgraph of G consisting of |E|— 5 3 edges.  ...  “The Four Traditions of Geography.” Journal of Geography, 63 (1964), 211-16. . Shaw, R. P. Migration Theory and Fact. Philadelphia: Regional Science Research Institute, 1975. . Taaffe, E. J.  ... 

Quantum Combinatorial Games: Structures and Computational Complexity [article]

Kyle Burke, Matthew Ferland, Shang-Hua Teng
2020 arXiv   pre-print
Our constructive proofs-both on the leap of complexity in concrete Quantum Nim and Quantum Undirected Geography and on the continuous collapses, in the quantum setting, of complexity in abstract PSPACE-complete  ...  Exploring Quantum Undirected Geography In this section, we will focus on Quantum Undirected Geography.  ...  Early, we considered Undirected Geography, a special case of Geography, in which the graph is undirected.  ... 
arXiv:2011.03704v1 fatcat:dguqcv3jy5ey3kjgax6knryg7u

The complexity of UNO [article]

Erik D. Demaine, Martin L. Demaine, Nicholas J. A. Harvey, Ryuhei Uehara, Takeaki Uno, Yushi Uno
2013 arXiv   pre-print
Among those, Directed Edge Geography [12] , Directed Vertex Geography [10] and Undirected Edge Geography [4] are known to be PSPACE-complete.  ...  Furthermore, Undirected Edge Geography remains PSPACE-complete even when the graph is planar, and Directed Edge/Vertex Geography remains PSPACE-complete even when the graph is planar or bipartite.  ... 
arXiv:1003.2851v3 fatcat:6lavnawwuzax5as6a4rkqboc3e
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