111 research outputs found
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 the Recognition of Fuzzy Circular Interval Graphs
Fuzzy circular interval graphs are a generalization of proper circular arc
graphs and have been recently introduced by Chudnovsky and Seymour as a
fundamental subclass of claw-free graphs. In this paper, we provide a
polynomial-time algorithm for recognizing such graphs, and more importantly for
building a suitable representation.Comment: 12 pages, 2 figure
How many matchings cover the nodes of a graph?
Given an undirected graph, are there matchings whose union covers all of
its nodes, that is, a matching--cover? A first, easy polynomial solution
from matroid union is possible, as already observed by Wang, Song and Yuan
(Mathematical Programming, 2014). However, it was not satisfactory neither from
the algorithmic viewpoint nor for proving graphic theorems, since the
corresponding matroid ignores the edges of the graph.
We prove here, simply and algorithmically: all nodes of a graph can be
covered with matchings if and only if for every stable set we have
. When , an exception occurs: this condition is not
enough to guarantee the existence of a matching--cover, that is, the
existence of a perfect matching, in this case Tutte's famous matching theorem
(J. London Math. Soc., 1947) provides the right `good' characterization. The
condition above then guarantees only that a perfect -matching exists, as
known from another theorem of Tutte (Proc. Amer. Math. Soc., 1953).
Some results are then deduced as consequences with surprisingly simple
proofs, using only the level of difficulty of bipartite matchings. We give some
generalizations, as well as a solution for minimization if the edge-weights are
non-negative, while the edge-cardinality maximization of matching--covers
turns out to be already NP-hard.
We have arrived at this problem as the line graph special case of a model
arising for manufacturing integrated circuits with the technology called
`Directed Self Assembly'.Comment: 10 page
Enhancing PGA Tour Performance: Leveraging ShotlinkTM Data for Optimization and Prediction
In this study, we demonstrate how data from the PGA Tour, combined with
stochastic shortest path models (MDPs), can be employed to refine the
strategies of professional golfers and predict future performances. We present
a comprehensive methodology for this objective, proving its computational
feasibility. This sets the stage for more in-depth exploration into leveraging
data available to professional and amateurs for strategic optimization and
forecasting performance in golf. For the replicability of our results, and to
adapt and extend the methodology and prototype solution, we provide access to
all our codes and analyses (R and C++)
Should Sports Professionals Consider Their Adversary's Strategy? A Case Study of Match Play in Golf
This study explores strategic considerations in professional golf's Match
Play format, challenging the conventional focus on individual performance.
Leveraging PGA Tour data, we investigate the impact of factoring in an
adversary's strategy. Our findings suggest that while slight strategy
adjustments can be advantageous in specific scenarios, the overall benefit of
considering an opponent's strategy remains modest. This confirms the common
wisdom in golf, reinforcing the recommendation to adhere to optimal stroke-play
strategies due to challenges in obtaining precise opponent statistics. We
believe that the methodology employed here could offer valuable insights into
whether opponents' performances should also be considered in other two-player
or team sports, such as tennis, darts, soccer, volleyball, etc. We hope that
this research will pave the way for new avenues of study in these areas
Horizontal collaboration in forestry: game theory models and algorithms for trading demands
In this paper, we introduce a new cooperative game theory model that we call
production-distribution game to address a major open problem for operations
research in forestry, raised by R\"onnqvist et al. in 2015, namely, that of
modelling and proposing efficient sharing principles for practical
collaboration in transportation in this sector. The originality of our model
lies in the fact that the value/strength of a player does not only depend on
the individual cost or benefit of the objects she owns but also depends on her
market shares (customers demand). We show however that the
production-distribution game is an interesting special case of a market game
introduced by Shapley and Shubik in 1969. As such it exhibits the nice property
of having a non-empty core. We then prove that we can compute both the
nucleolus and the Shapley value efficiently, in a nontrivial and interesting
special case. We in particular provide two different algorithms to compute the
nucleolus: a simple separation algorithm and a fast primal-dual algorithm. Our
results can be used to tackle more general versions of the problem and we
believe that our contribution paves the way towards solving the challenging
open problem herein
On non-rank facets of the stable set polytope of claw-free graphs and circulant graphs
We deal with non-rank facets of the stable set polytope of claw-free graphs. We extend results of Giles and Trotter [7] by (i) showing that for any nonnegative integer a there exists a circulant graph whose stable set polytope has a facet-inducing inequality with (a,a+1)-valued coefficients (rank facets have only coefficients 0, 1), and (ii) providing new facets of the stable set polytope with up to five different non-zero coefficients for claw-free graphs. We prove that coefficients have to be consecutive in any facet with exactly two different non-zero coefficients (assuming they are relatively prime). Last but not least, we present a complete description of the stable set polytope for graphs with stability number 2, already observed by Cook [3] and Shepherd [18
DSA-aware multiple patterning for the manufacturing of vias: Connections to graph coloring problems, IP formulations, and numerical experiments
In this paper, we investigate the manufacturing of vias in integrated
circuits with a new technology combining lithography and Directed Self Assembly
(DSA). Optimizing the production time and costs in this new process entails
minimizing the number of lithography steps, which constitutes a generalization
of graph coloring. We develop integer programming formulations for several
variants of interest in the industry, and then study the computational
performance of our formulations on true industrial instances. We show that the
best integer programming formulation achieves good computational performance,
and indicate potential directions to further speed-up computational time and
develop exact approaches feasible for production
Debris Disks of Members of the Blanco 1 Open Cluster
We have used the Spitzer Space Telescope to obtain Multiband Imaging
Photometer for Spitzer (MIPS) 24 um photometry for 37 members of the ~100 Myr
old open cluster Blanco 1. For the brightest 25 of these stars (where we have
3sigma uncertainties less than 15%), we find significant mid-IR excesses for
eight stars, corresponding to a debris disk detection frequency of about 32%.
The stars with excesses include two A stars, four F dwarfs and two G dwarfs.
The most significant linkage between 24 um excess and any other stellar
property for our Blanco 1 sample of stars is with binarity. Blanco 1 members
that are photometric binaries show few or no detected 24 um excesses whereas a
quarter of the apparently single Blanco 1 members do have excesses. We have
examined the MIPS data for two other clusters of similar age to Blanco 1 -- NGC
2547 and the Pleiades. The AFGK photometric binary star members of both of
these clusters also show a much lower frequency of 24 um excesses compared to
stars that lie near the single-star main sequence. We provide a new
determination of the relation between V-Ks color and Ks-[24] color for main
sequence photospheres based on Hyades members observed with MIPS. As a result
of our analysis of the Hyades data, we identify three low mass Hyades members
as candidates for having debris disks near the MIPS detection limit.Comment: Accepted to Ap
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