13 research outputs found
Constraint Satisfaction Problems over Numeric Domains
We present a survey of complexity results for constraint satisfaction problems (CSPs) over the integers, the rationals, the reals, and the complex numbers. Examples of such problems are feasibility of linear programs, integer linear programming, the max-atoms problem, Hilbert\u27s tenth problem, and many more. Our particular focus is to identify those CSPs that can be solved in polynomial time, and to distinguish them from CSPs that are NP-hard. A very helpful tool for obtaining complexity classifications in this context is the concept of a polymorphism from universal algebra
Signed tropicalization of polar cones
We study the tropical analogue of the notion of polar of a cone, working over
the semiring of tropical numbers with signs. We characterize the cones which
arise as polars of sets of tropically nonnegative vectors by an invariance
property with respect to a tropical analogue of Fourier-Motzkin elimination. We
also relate tropical polars with images by the nonarchimedean valuation of
classical polars over real closed nonarchimedean fields and show, in
particular, that for semi-algebraic sets over such fields, the operation of
taking the polar commutes with the operation of signed valuation (keeping track
both of the nonarchimedean valuation and sign). We apply these results to
characterize images by the signed valuation of classical cones of matrices,
including the cones of positive semidefinite matrices, completely positive
matrices, completely positive semidefinite matrices, and their polars,
including the cone of co-positive matrices, showing that hierarchies of
classical cones collapse under tropicalization. We finally discuss an
application of these ideas to optimization with signed tropical numbers.Comment: 24 pages, 1 figure. Changes with respect to Version 2: we improved
Introduction and added Examples 3.24 and 3.25 illustrating that "bend
addition" can be considered as a tropical analogue of the Fourier-Motzkin
eliminatio
Tropically convex constraint satisfaction
A semilinear relation S is max-closed if it is preserved by taking the
componentwise maximum. The constraint satisfaction problem for max-closed
semilinear constraints is at least as hard as determining the winner in Mean
Payoff Games, a notorious problem of open computational complexity. Mean Payoff
Games are known to be in the intersection of NP and co-NP, which is not known
for max-closed semilinear constraints. Semilinear relations that are max-closed
and additionally closed under translations have been called tropically convex
in the literature. One of our main results is a new duality for open tropically
convex relations, which puts the CSP for tropically convex semilinaer
constraints in general into NP intersected co-NP. This extends the
corresponding complexity result for scheduling under and-or precedence
constraints, or equivalently the max-atoms problem. To this end, we present a
characterization of max-closed semilinear relations in terms of syntactically
restricted first-order logic, and another characterization in terms of a finite
set of relations L that allow primitive positive definitions of all other
relations in the class. We also present a subclass of max-closed constraints
where the CSP is in P; this class generalizes the class of max-closed
constraints over finite domains, and the feasibility problem for max-closed
linear inequalities. Finally, we show that the class of max-closed semilinear
constraints is maximal in the sense that as soon as a single relation that is
not max-closed is added to L, the CSP becomes NP-hard.Comment: 29 pages, 2 figure
Recommended from our members
Reelle Algebraische Geometrie
This workshop was organized by Michel Coste (Rennes), Claus Scheiderer (Konstanz) and Niels Schwartz (Passau). The talks focussed on recent developments in real enumerative and tropical geometry, positivity and sums of squares, real aspects of classical algebraic geometry, semialgebraic and tame geometry, and topology and singularities of real varieties
Recommended from our members
Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability
Continuing the tradition initiated in the MFO workshops held in 2014 and 2017, this workshop was dedicated to the newest developments in real algebraic geometry and polynomial optimization, with a particular emphasis on free non-commutative real algebraic geometry and hyperbolic programming. A particular effort was invested in exploring the interrelations with free probability. This established an interesting dialogue between researchers working in real algebraic geometry and those working in free probability, from which emerged new exciting and promising synergies
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Factors Influencing Customer Satisfaction towards E-shopping in Malaysia
Online shopping or e-shopping has changed the world of business and quite a few people have
decided to work with these features. What their primary concerns precisely and the responses from
the globalisation are the competency of incorporation while doing their businesses. E-shopping has
also increased substantially in Malaysia in recent years. The rapid increase in the e-commerce
industry in Malaysia has created the demand to emphasize on how to increase customer satisfaction
while operating in the e-retailing environment. It is very important that customers are satisfied with
the website, or else, they would not return. Therefore, a crucial fact to look into is that companies
must ensure that their customers are satisfied with their purchases that are really essential from the ecommerce’s
point of view. With is in mind, this study aimed at investigating customer satisfaction
towards e-shopping in Malaysia. A total of 400 questionnaires were distributed among students
randomly selected from various public and private universities located within Klang valley area.
Total 369 questionnaires were returned, out of which 341 questionnaires were found usable for
further analysis. Finally, SEM was employed to test the hypotheses. This study found that customer
satisfaction towards e-shopping in Malaysia is to a great extent influenced by ease of use, trust,
design of the website, online security and e-service quality. Finally, recommendations and future
study direction is provided.
Keywords: E-shopping, Customer satisfaction, Trust, Online security, E-service quality, Malaysia