12,356 research outputs found
Homomorphisms of binary Cayley graphs
A binary Cayley graph is a Cayley graph based on a binary group. In 1982,
Payan proved that any non-bipartite binary Cayley graph must contain a
generalized Mycielski graph of an odd-cycle, implying that such a graph cannot
have chromatic number 3. We strengthen this result first by proving that any
non-bipartite binary Cayley graph must contain a projective cube as a subgraph.
We further conjecture that any homo- morphism of a non-bipartite binary Cayley
graph to a projective cube must be surjective and we prove some special case of
this conjecture
Studies of MCP-PMTs in the miniTimeCube neutrino detector
This report highlights two different types of cross-talk in the
photodetectors of the miniTimeCube neutrino experiment. The miniTimeCube
detector has 24 -anode Photonis MCP-PMTs Planacon XP85012,
totalling 1536 individual pixels viewing the 2-liter cube of plastic
scintillator
Belt distance between facets of space-filling zonotopes
For every d-dimensional polytope P with centrally symmetric facets we can
associate a "subway map" such that every line of this "subway" corresponds to
set of facets parallel to one of ridges P. The belt diameter of P is the
maximal number of line changes that you need to do in order to get from one
station to another.
In this paper we prove that belt diameter of d-dimensional space-filling
zonotope is not greater than . Moreover we show
that this bound can not be improved in dimensions d at most 6.Comment: 17 pages, 5 figure
Lower Bounds for Oblivious Near-Neighbor Search
We prove an lower bound on the dynamic
cell-probe complexity of statistically
approximate-near-neighbor search () over the -dimensional
Hamming cube. For the natural setting of , our result
implies an lower bound, which is a quadratic
improvement over the highest (non-oblivious) cell-probe lower bound for
. This is the first super-logarithmic
lower bound for against general (non black-box) data structures.
We also show that any oblivious data structure for
decomposable search problems (like ) can be obliviously dynamized
with overhead in update and query time, strengthening a classic
result of Bentley and Saxe (Algorithmica, 1980).Comment: 28 page
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