To save this undefined to your undefined account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your undefined account.
Find out more about saving content to .
To save this article to your Kindle, first ensure email@example.com is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
The traveling salesman problem is one of the most important problems in operations
research, especially when additional precedence constraints are considered. Here, we
consider the well-known variant where a linear order on k special vertices is given
that has to be preserved in any feasible Hamiltonian cycle. This problem is called Ordered
TSP and we consider it on input instances where the edge-cost function satisfies a
triangle inequality, i.e., where the length of a direct edge cannot
exceed the cost of any detour via a third vertex by more than a factor of
β> 1. We
design two new polynomial-time approximation algorithms for this problem. The first
algorithm essentially improves over the best previously known algorithm for almost all
values of k
1.087889. The second algorithm gives a further improvement for
2n ≥ 11k +
7 and β< √34/3 , where n is the number of vertices in the graph.
A Hamming compatible metric is an integer-valued metric on the words of a finite alphabet
which agrees with the usual Hamming distance for words of equal length. We define a new
Hamming compatible metric and show this metric is minimal in the class of all
“well-behaved” Hamming compatible metrics. This gives a negative answer to a question
stated by Echi in his paper [O. Echi, Appl. Math. Sci. (Ruse) 3
We present a new model of a two-dimensional computing device called Sgraffito
automaton. In general, the model is quite simple, which allows a clear design
of computations. When restricted to one-dimensional inputs, that is, strings, the
Sgraffito automaton does not exceed the power of finite-state automata. On the other hand,
for two-dimensional inputs, it yields a family of picture languages with good closure
properties that strictly includes the class REC of recognizable picture languages. The
deterministic Sgraffito automata define a class of picture languages that includes the
class of deterministic recognizable picture languages DREC, the class of picture languages
that are accepted by four-way alternating automata, those that are accepted by
deterministic one-marker automata, and the sudoku-deterministically recognizable picture
languages, but the membership problem for the accepted languages is still decidable in
polynomial time. In addition, the deterministic Sgraffito automata accept some unary
picture languages that are outside of the class REC.
The minimum roman dominating problem (denoted by γR(G),
the weight of minimum roman dominating function of graph G) is a variant of the very
well known minimum dominating set problem (denoted by γ(G), the
cardinality of minimum dominating set of graph G). Both problems remain NP-Complete when restricted
to P5-free graph class [A.A. Bertossi,
Inf. Process. Lett. 19 (1984) 37–40; E.J. Cockayne,
et al. Discret. Math. 278 (2004) 11–22]. In this paper we
study both problems restricted to some subclasses of P5-free graphs.
We describe robust algorithms that solve both problems restricted to (P5,(s,t)-net)-free graphs
in polynomial time. This result generalizes previous works for both problems, and improves
existing algorithms when restricted to certain families such as (P5,bull)-free
graphs. It turns out that the same approach also serves to solve problems for general
graphs in polynomial time whenever γ(G) and γR(G)
are fixed (more efficiently than naive algorithms). Moreover, the algorithms described are
extremely simple which makes them useful for practical purposes, and as we show in the
last section it allows to simplify algorithms for significant classes such as