199 research outputs found
Probability Distributions on Partially Ordered Sets and Network Interdiction Games
This article poses the following problem: Does there exist a probability
distribution over subsets of a finite partially ordered set (poset), such that
a set of constraints involving marginal probabilities of the poset's elements
and maximal chains is satisfied? We present a combinatorial algorithm to
positively resolve this question. The algorithm can be implemented in
polynomial time in the special case where maximal chain probabilities are
affine functions of their elements. This existence problem is relevant for the
equilibrium characterization of a generic strategic interdiction game on a
capacitated flow network. The game involves a routing entity that sends its
flow through the network while facing path transportation costs, and an
interdictor who simultaneously interdicts one or more edges while facing edge
interdiction costs. Using our existence result on posets and strict
complementary slackness in linear programming, we show that the Nash equilibria
of this game can be fully described using primal and dual solutions of a
minimum-cost circulation problem. Our analysis provides a new characterization
of the critical components in the interdiction game. It also leads to a
polynomial-time approach for equilibrium computation
Network Interdiction Using Adversarial Traffic Flows
Traditional network interdiction refers to the problem of an interdictor
trying to reduce the throughput of network users by removing network edges. In
this paper, we propose a new paradigm for network interdiction that models
scenarios, such as stealth DoS attack, where the interdiction is performed
through injecting adversarial traffic flows. Under this paradigm, we first
study the deterministic flow interdiction problem, where the interdictor has
perfect knowledge of the operation of network users. We show that the problem
is highly inapproximable on general networks and is NP-hard even when the
network is acyclic. We then propose an algorithm that achieves a logarithmic
approximation ratio and quasi-polynomial time complexity for acyclic networks
through harnessing the submodularity of the problem. Next, we investigate the
robust flow interdiction problem, which adopts the robust optimization
framework to capture the case where definitive knowledge of the operation of
network users is not available. We design an approximation framework that
integrates the aforementioned algorithm, yielding a quasi-polynomial time
procedure with poly-logarithmic approximation ratio for the more challenging
robust flow interdiction. Finally, we evaluate the performance of the proposed
algorithms through simulations, showing that they can be efficiently
implemented and yield near-optimal solutions
REVISITING COORDINATED SUBMARINE TACTICS USING MODERN COMPUTATIONAL METHODS
Current doctrine has largely discarded the use of coordinated submarine tactics (known as Wolfpack tactics) due to the complexity of inter-pack and intra-pack coordination. However, recent advancements in technology may greatly increase the feasibility of secure communication between submarines operating in a Wolfpack. Agent-based modeling is used to simulate the behavior of submarines operating in a wartime environment at sea. Three secure communication availabilities are represented: no communication between submarines, communication every 10 hours, and constant secure communication. Three types of wartime environments are considered: submarines hunting transiting merchants, submarines hunting transiting warships in an environment with neutral shipping, and submarines hunting transiting warships operating as a Surface Action Group (SAG) with neutral shipping. Effectiveness is measured as âyield,â which is the average number of target kills as a function of the number of submarines in the Wolfpack. The simulation results stress that the success of Wolfpack tactics increasingly depends upon secure submarine communication and situational awareness with the growth of neutral shipping in the wartime environment.Outstanding ThesisLieutenant, United States NavyApproved for public release. Distribution is unlimited
Improved Hardness for Cut, Interdiction, and Firefighter Problems
We study variants of the classic s-t cut problem and prove the following improved hardness results assuming the Unique Games Conjecture (UGC).
* For Length-Bounded Cut and Shortest Path Interdiction, we show that both problems are hard to approximate within any constant factor, even if we allow bicriteria approximation. If we want to cut vertices or the graph is directed, our hardness ratio for Length-Bounded Cut matches the best approximation ratio up to a constant. Previously, the best hardness ratio was 1.1377 for Length-Bounded Cut and 2 for Shortest Path Interdiction.
* For any constant k >= 2 and epsilon > 0, we show that Directed Multicut with k source-sink pairs is hard to approximate within a factor k - epsilon. This matches the trivial k-approximation algorithm. By a simple reduction, our result for k = 2 implies that Directed Multiway Cut with two terminals (also known as s-t Bicut} is hard to approximate within a factor 2 - epsilon, matching the trivial 2-approximation algorithm.
* Assuming a variant of the UGC (implied by another variant of Bansal and Khot), we prove that it is hard to approximate Resource Minimization Fire Containment within any constant factor. Previously, the best hardness ratio was 2. For directed layered graphs with b layers, our hardness ratio Omega(log b) matches the best approximation algorithm.
Our results are based on a general method of converting an integrality gap instance to a length-control dictatorship test for variants of the s-t cut problem, which may be useful for other problems
The ethics of New Development Economics: is the Experimental Approach to Development Economics morally wrong?
ArticleThe 2000s have witnessed the arrival and growing popularity of randomized controlled experiments (RCTs) in Development Economics. Whilst this new way of conducting research on development has unfolded important insights, the ethical challenge it provokes has not yet been systematically examined. The present article aims at filling this gap by providing the first ad hoc discussion of the moral issues that accompany the use of RCTs in Development Economics. Claiming that this new research agenda needs its own, specific set of ethical guidelines, we expose the six ethical problems that these experiments potentially provoke and that should therefore be carefully assessed by ethics committees before an RCT is launched and by scholarly journals before its results are published
Robust randomized matchings
The following game is played on a weighted graph: Alice selects a matching
and Bob selects a number . Alice's payoff is the ratio of the weight of
the heaviest edges of to the maximum weight of a matching of size at
most . If guarantees a payoff of at least then it is called
-robust. In 2002, Hassin and Rubinstein gave an algorithm that returns
a -robust matching, which is best possible.
We show that Alice can improve her payoff to by playing a
randomized strategy. This result extends to a very general class of
independence systems that includes matroid intersection, b-matchings, and
strong 2-exchange systems. It also implies an improved approximation factor for
a stochastic optimization variant known as the maximum priority matching
problem and translates to an asymptotic robustness guarantee for deterministic
matchings, in which Bob can only select numbers larger than a given constant.
Moreover, we give a new LP-based proof of Hassin and Rubinstein's bound
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