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Accommodating user preferences in the optimization of public transport travel
The Stochastic Shortest Path Problem : A polyhedral combinatorics perspective
In this paper, we give a new framework for the stochastic shortest path
problem in finite state and action spaces. Our framework generalizes both the
frameworks proposed by Bertsekas and Tsitsikli and by Bertsekas and Yu. We
prove that the problem is well-defined and (weakly) polynomial when (i) there
is a way to reach the target state from any initial state and (ii) there is no
transition cycle of negative costs (a generalization of negative cost cycles).
These assumptions generalize the standard assumptions for the deterministic
shortest path problem and our framework encapsulates the latter problem (in
contrast with prior works). In this new setting, we can show that (a) one can
restrict to deterministic and stationary policies, (b) the problem is still
(weakly) polynomial through linear programming, (c) Value Iteration and Policy
Iteration converge, and (d) we can extend Dijkstra's algorithm
On green routing and scheduling problem
The vehicle routing and scheduling problem has been studied with much
interest within the last four decades. In this paper, some of the existing
literature dealing with routing and scheduling problems with environmental
issues is reviewed, and a description is provided of the problems that have
been investigated and how they are treated using combinatorial optimization
tools
Finding approximate palindromes in strings
We introduce a novel definition of approximate palindromes in strings, and
provide an algorithm to find all maximal approximate palindromes in a string
with up to errors. Our definition is based on the usual edit operations of
approximate pattern matching, and the algorithm we give, for a string of size
on a fixed alphabet, runs in time. We also discuss two
implementation-related improvements to the algorithm, and demonstrate their
efficacy in practice by means of both experiments and an average-case analysis
Cellular Automata Applications in Shortest Path Problem
Cellular Automata (CAs) are computational models that can capture the
essential features of systems in which global behavior emerges from the
collective effect of simple components, which interact locally. During the last
decades, CAs have been extensively used for mimicking several natural processes
and systems to find fine solutions in many complex hard to solve computer
science and engineering problems. Among them, the shortest path problem is one
of the most pronounced and highly studied problems that scientists have been
trying to tackle by using a plethora of methodologies and even unconventional
approaches. The proposed solutions are mainly justified by their ability to
provide a correct solution in a better time complexity than the renowned
Dijkstra's algorithm. Although there is a wide variety regarding the
algorithmic complexity of the algorithms suggested, spanning from simplistic
graph traversal algorithms to complex nature inspired and bio-mimicking
algorithms, in this chapter we focus on the successful application of CAs to
shortest path problem as found in various diverse disciplines like computer
science, swarm robotics, computer networks, decision science and biomimicking
of biological organisms' behaviour. In particular, an introduction on the first
CA-based algorithm tackling the shortest path problem is provided in detail.
After the short presentation of shortest path algorithms arriving from the
relaxization of the CAs principles, the application of the CA-based shortest
path definition on the coordinated motion of swarm robotics is also introduced.
Moreover, the CA based application of shortest path finding in computer
networks is presented in brief. Finally, a CA that models exactly the behavior
of a biological organism, namely the Physarum's behavior, finding the
minimum-length path between two points in a labyrinth is given.Comment: To appear in the book: Adamatzky, A (Ed.) Shortest path solvers. From
software to wetware. Springer, 201
FollowMe: Efficient Online Min-Cost Flow Tracking with Bounded Memory and Computation
One of the most popular approaches to multi-target tracking is
tracking-by-detection. Current min-cost flow algorithms which solve the data
association problem optimally have three main drawbacks: they are
computationally expensive, they assume that the whole video is given as a
batch, and they scale badly in memory and computation with the length of the
video sequence. In this paper, we address each of these issues, resulting in a
computationally and memory-bounded solution. First, we introduce a dynamic
version of the successive shortest-path algorithm which solves the data
association problem optimally while reusing computation, resulting in
significantly faster inference than standard solvers. Second, we address the
optimal solution to the data association problem when dealing with an incoming
stream of data (i.e., online setting). Finally, we present our main
contribution which is an approximate online solution with bounded memory and
computation which is capable of handling videos of arbitrarily length while
performing tracking in real time. We demonstrate the effectiveness of our
algorithms on the KITTI and PETS2009 benchmarks and show state-of-the-art
performance, while being significantly faster than existing solvers
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