25 research outputs found
The analysis of split graphs in social networks based on the K-Cardinality assignment problem
In terms of social networks, split graphs correspond to the variety of interpersonal and
intergroup relations. In this paper we analyse the interaction between the cliques (socially strong
and trusty groups) and the independent sets (fragmented and non-connected groups of people) as
the basic components of any split graph. Based on the Semi-Lagrangean relaxation for the kcardinality
assignment problem, we show the way of minimizing the socially risky interactions
between the cliques and the independent sets within the social network
Revisiting the Evolution and Application of Assignment Problem: A Brief Overview
The assignment problem (AP) is incredibly challenging that can model many real-life problems. This paper provides a limited review of the recent developments that have appeared in the literature, meaning of assignment problem as well as solving techniques and will provide a review on  a lot of research studies on different types of assignment problem taking place in present day real life situation in order to capture the variations in different types of assignment techniques. Keywords: Assignment problem, Quadratic Assignment, Vehicle Routing, Exact Algorithm, Bound, Heuristic etc
Zero-Assignment Constraint for Graph Matching with Outliers
Graph matching (GM), as a longstanding problem in computer vision and pattern
recognition, still suffers from numerous cluttered outliers in practical
applications. To address this issue, we present the zero-assignment constraint
(ZAC) for approaching the graph matching problem in the presence of outliers.
The underlying idea is to suppress the matchings of outliers by assigning
zero-valued vectors to the potential outliers in the obtained optimal
correspondence matrix. We provide elaborate theoretical analysis to the
problem, i.e., GM with ZAC, and figure out that the GM problem with and without
outliers are intrinsically different, which enables us to put forward a
sufficient condition to construct valid and reasonable objective function.
Consequently, we design an efficient outlier-robust algorithm to significantly
reduce the incorrect or redundant matchings caused by numerous outliers.
Extensive experiments demonstrate that our method can achieve the
state-of-the-art performance in terms of accuracy and efficiency, especially in
the presence of numerous outliers
Polynomial convolutions in max-plus algebra
Recently, in a work that grew out of their exploration of interlacing
polynomials, Marcus, Spielman and Srivastava and then Marcus studied certain
combinatorial polynomial convolutions. These convolutions preserve
real-rootedness and capture expectations of characteristic polynomials of
unitarily invariant random matrices, thus providing a link to free probability.
We explore analogues of these types of convolutions in the setting of max-plus
algebra. In this setting the max-permanent replaces the determinant, the
maximum is the analogue of the expected value and real-rootedness is replaced
by full canonical form. Our results resemble those of Marcus et al., however,
in contrast to the classical setting we obtain an exact and simple description
of all roots.Comment: 27 page
Profit Maximization with Sufficient Customer Satisfactions
In many commercial campaigns, we observe that there exists a tradeoff between the number of customers satisfied by the company and the profit gained. Merely satisfying as many customers as possible or maximizing the profit is not desirable. To this end, in this article, we propose a new problem called
k
-
<underline>S</underline>atisfiability <underline>A</underline>ssignment for <underline>M</underline>aximizing the <underline>P</underline>rofit
(
k
-SAMP), where
k
is a user parameter and a non-negative integer. Given a set
P
of products and a set
O
of customers,
k
-SAMP is to find an assignment between
P
and
O
such that at least
k
customers are satisfied in the assignment and the profit incurred by this assignment is maximized. Although we find that this problem is closely related to two classic computer science problems, namely maximum weight matching and maximum matching, the techniques developed for these classic problems cannot be adapted to our
k
-SAMP problem. In this work, we design a novel algorithm called
Adjust
for the
k
-SAMP problem. Given an assignment
A
,
Adjust
iteratively increases the profit of
A
by
adjusting
some appropriate matches in
A
while keeping at least
k
customers satisfied in
A
. We prove that
Adjust
returns a global optimum. Extensive experiments were conducted that verified the efficiency of
Adjust
.
</jats:p
Bi-level optimisation and machine learning in the management of large service-oriented field workforces.
The tactical planning problem for members of the service industry with large multi-skilled workforces is an important process that is often underlooked. It sits between the operational plan - which involves the actual allocation of members of the workforce to tasks - and the strategic plan where long term visions are set. An accurate tactical plan can have great benefits to service organisations and this is something we demonstrate in this work. Sitting where it does, it is made up of a mix of forecast and actual data, which can make effectively solving the problem difficult. In members of the service industry with large multi-skilled workforces it can often become a very large problem very quickly, as the number of decisions scale quickly with the number of elements within the plan. In this study, we first update and define the tactical planning problem to fit the process currently undertaken manually in practice. We then identify properties within the problem that identify it as a new candidate for the application of bi-level optimisation techniques. The tactical plan is defined in the context of a pair of leader-follower linked sub-models, which we show to be solvable to produce automated solutions to the tactical plan. We further identify the need for the use of machine learning techniques to effectively find solutions in practical applications, where limited detail is available in the data due to its forecast nature. We develop neural network models to solve this issue and show that they provide more accurate results than the current planners. Finally, we utilise them as a surrogate for the follower in the bi-level framework to provide real world applicable solutions to the tactical planning problem. The models developed in this work have already begun to be deployed in practice and are providing significant impact. This is along with identifying a new application area for bi-level modelling techniques