112 research outputs found
VLSI layouts and DNA physical mappings
We show that an important problem (-ICG) in computational biology is
equivalent to a colored version of a well-known graph layout problem (-CVS).Comment: 7 page
The complexity of broadcasting in bounded-degree networks
Broadcasting concerns the dissemination of a message originating at one node
of a network to all other nodes. This task is accomplished by placing a series
of calls over the communication lines of the network between neighboring nodes,
where each call requires a unit of time and a call can involve only two nodes.
We show that for bounded-degree networks determining the minimum broadcast time
from an originating node remains NP-complete.Comment: 6 page
New results for the degree/diameter problem
The results of computer searches for large graphs with given (small) degree
and diameter are presented. The new graphs are Cayley graphs of semidirect
products of cyclic groups and related groups. One fundamental use of our
``dense graphs'' is in the design of efficient communication network
topologies.Comment: 15 page
A simple linear-time algorithm for finding path-decompositions of small width
We described a simple algorithm running in linear time for each fixed
constant , that either establishes that the pathwidth of a graph is
greater than , or finds a path-decomposition of of width at most
. This provides a simple proof of the result by Bodlaender that many
families of graphs of bounded pathwidth can be recognized in linear time.Comment: 9 page
Obstructions to within a few vertices or edges of acyclic
Finite obstruction sets for lower ideals in the minor order are guaranteed to
exist by the Graph Minor Theorem. It has been known for several years that, in
principle, obstruction sets can be mechanically computed for most natural lower
ideals. In this paper, we describe a general-purpose method for finding
obstructions by using a bounded treewidth (or pathwidth) search. We illustrate
this approach by characterizing certain families of cycle-cover graphs based on
the two well-known problems: -{\sc Feedback Vertex Set} and -{\sc
Feedback Edge Set}. Our search is based on a number of algorithmic strategies
by which large constants can be mitigated, including a randomized strategy for
obtaining proofs of minimality.Comment: 16 page
Computing A Glimpse of Randomness
A Chaitin Omega number is the halting probability of a universal Chaitin
(self-delimiting Turing) machine. Every Omega number is both computably
enumerable (the limit of a computable, increasing, converging sequence of
rationals) and random (its binary expansion is an algorithmic random sequence).
In particular, every Omega number is strongly non-computable. The aim of this
paper is to describe a procedure, which combines Java programming and
mathematical proofs, for computing the exact values of the first 64 bits of a
Chaitin Omega:
0000001000000100000110001000011010001111110010111011101000010000. Full
description of programs and proofs will be given elsewhere.Comment: 16 pages; Experimental Mathematics (accepted
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