The complexity of minimizing wire lengths in VLSI layouts
Information Processing Letters
String graphs. II.: Recognizing string graphs is NP-hard
Journal of Combinatorial Theory Series B
String graphs requiring exponential representations
Journal of Combinatorial Theory Series B
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
The VLSI layout problem in various embedding models
WG '90 Proceedings of the 16th international workshop on Graph-theoretic concepts in computer science
A special planar satisfiability problem and a consequence of its NP-completeness
Discrete Applied Mathematics
Embeddings of complete binary trees into grids and extended grids with total vertex-congestion
Discrete Applied Mathematics
Nearest Neighbour Graph Realizability is NP-hard
LATIN '95 Proceedings of the Second Latin American Symposium on Theoretical Informatics
VLSI layout of trees into grids of minimum width
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Expansion of layouts of complete binary trees into grids
Discrete Applied Mathematics
Recognizing string graphs in NP
Journal of Computer and System Sciences - STOC 2002
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Graph Drawing
Bend-bounded path intersection graphs: sausages, noodles, and waffles on a grill
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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We investigate embeddings of graphs into the infinite extended grid graph. The problem was motivated by computation on adiabatic quantum computers, but it is related to a number of other well studied grid embedding problems. Such problems typically deal with representing vertices by grid points, and edges by grid paths, while minimizing some objective function such as the area or the maximum length of the grid paths representing the edges. Our particular model, while expressible in this language, is more naturally viewed as one where the vertices are represented by subtrees of the grid (called islands), and the edges are represented by the usual grid edges joining the islands. Somewhat unexpectedly, these graphs turn out to unify such seemingly unrelated graph classes as the string graphs and the induced subgraphs of the extended grid. The connection is established by limiting the size (number of vertices) k of the representing islands. We study the problem of representability of an input graph G by islands of size at most k. We conjecture that this problem is NP-complete for any positive integer k, and prove the conjecture for kk5; the cases k=3, 4, 5 remain open.