4,720 research outputs found
Collapsibility to a subcomplex of a given dimension is NP-complete
In this paper we extend the works of Tancer and of Malgouyres and Franc\'es,
showing that -collapsibility is NP-complete for except
. By -collapsibility we mean the following problem: determine
whether a given -dimensional simplicial complex can be collapsed to some
-dimensional subcomplex. The question of establishing the complexity status
of -collapsibility was asked by Tancer, who proved NP-completeness of
and -collapsibility (for ). Our extended result,
together with the known polynomial-time algorithms for and ,
answers the question completely
The Complexity of Quantified Constraint Satisfaction: Collapsibility, Sink Algebras, and the Three-Element Case
The constraint satisfaction probem (CSP) is a well-acknowledged framework in
which many combinatorial search problems can be naturally formulated. The CSP
may be viewed as the problem of deciding the truth of a logical sentence
consisting of a conjunction of constraints, in front of which all variables are
existentially quantified. The quantified constraint satisfaction problem (QCSP)
is the generalization of the CSP where universal quantification is permitted in
addition to existential quantification. The general intractability of these
problems has motivated research studying the complexity of these problems under
a restricted constraint language, which is a set of relations that can be used
to express constraints.
This paper introduces collapsibility, a technique for deriving positive
complexity results on the QCSP. In particular, this technique allows one to
show that, for a particular constraint language, the QCSP reduces to the CSP.
We show that collapsibility applies to three known tractable cases of the QCSP
that were originally studied using disparate proof techniques in different
decades: Quantified 2-SAT (Aspvall, Plass, and Tarjan 1979), Quantified
Horn-SAT (Karpinski, Kleine B\"{u}ning, and Schmitt 1987), and Quantified
Affine-SAT (Creignou, Khanna, and Sudan 2001). This reconciles and reveals
common structure among these cases, which are describable by constraint
languages over a two-element domain. In addition to unifying these known
tractable cases, we study constraint languages over domains of larger size
Simpson's Paradox and Collapsibility
Simpson's paradox and collapsibility are two closely related concepts in the
context of data analysis. While the knowledge about the occurrence of Simpson's
paradox helps a statistician to draw correct and meaningful conclusions, the
concept of collapsibility deals with dimension-reduction aspects, when
Simpson's paradox does not occur. We discuss in this paper in some detail the
nature and the genesis of Simpson's paradox with respect to well-known examples
and also various concepts of collapsiblity. The main aim is to bring out the
close connections between these two phenomena, especially with regard to the
analysis of contingency tables, regression models and a certain measure of
association or a dependence function. There is a vast literature on these
topics and so we focus only on certain aspects, recent developments and some
important results in the above-mentioned areas.Comment: 19 page
Effects of variation in water content, clay fraction and sodium carbonate additions on the synthetic moulding properties of Igbokoda clay and silica sand
Loto, C.A. and Adebayo, H., 1990. Effects of variation in water content, clay fraction and sodium
carbonate additions on the synthetic moulding properties of Igbokoda clay and silica sand. Appl.
Clay Sci., 5: 165-181.
In this investigation, the Igbokoda pure silica sand is characterised and used as a base sand for the
Igbokoda clay- sand mixture in an attempt to develop an efficient synthetic moulding sand. The mechanical
properties of the clay-sand-water mixture were determined. The effect of additions ofNa2C03
to the moulding sand was examined with particular attention to its influence on mechanical properties
of the synthetic moulding sand. The fineness number, screen bulk fraction, total coarse fraction and
the total fine fraction of Igbokoda silica sand were found to be within the range that could give good
mouldable properties. The values obtained for the green compressive strength, the dry compressive
strength, the green and dry shear strengths, collapsibility and toughness indicate that Igbokoda clay
has good values as a binder for synthetic moulding sand. In general, the addition of Na2C03 gives improved properties to the moulding sand though with a tendency towards impaired collapsibility
values
- …