scholarly journals Accomplice Manipulation of the Deferred Acceptance Algorithm

2021 ◽  
Author(s):  
Hadi Hosseini ◽  
Fatima Umar ◽  
Rohit Vaish
Keyword(s):  
Strategic Behavior ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Matching Problem ◽  
Structural Result ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Novel Model ◽  
Manipulation Strategy

The deferred acceptance algorithm is an elegant solution to the stable matching problem that guarantees optimality and truthfulness for one side of the market. Despite these desirable guarantees, it is susceptible to strategic misreporting of preferences by the agents on the other side. We study a novel model of strategic behavior under the deferred acceptance algorithm: manipulation through an accomplice. Here, an agent on the proposed-to side (say, a woman) partners with an agent on the proposing side---an accomplice---to manipulate on her behalf (possibly at the expense of worsening his match). We show that the optimal manipulation strategy for an accomplice comprises of promoting exactly one woman in his true list (i.e., an inconspicuous manipulation). This structural result immediately gives a polynomial-time algorithm for computing an optimal accomplice manipulation. We also study the conditions under which the manipulated matching is stable with respect to the true preferences. Our experimental results show that accomplice manipulation outperforms self manipulation both in terms of the frequency of occurrence as well as the quality of matched partners.

scholarly journals What's the Matter with Tie-Breaking? Improving Efficiency in School Choice

2008 ◽  
Vol 98 (3) ◽  
pp. 669-689 ◽  
Author(s):  
Aytek Erdil ◽  
Haluk Ergin
Keyword(s):  
United States ◽  
School Choice ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
The United States ◽  
Stable Mechanism ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Stable Improvement

In several school choice districts in the United States, the student proposing deferred acceptance algorithm is applied after indifferences in priority orders are broken in some exogenous way. Although such a tie-breaking procedure preserves stability, it adversely affects the welfare of the students since it introduces artificial stability constraints. Our main finding is a polynomial-time algorithm for the computation of a student-optimal stable matching when priorities are weak. The idea behind our construction relies on a new notion which we call a stable improvement cycle. We also investigate the strategic properties of the student-optimal stable mechanism. (JEL C78, D82, I21)

More Flexible Curve Matching via the Partial Fréchet Similarity

2016 ◽  
Vol 26 (01) ◽  
pp. 33-52 ◽  
Author(s):  
Christian Scheffer
Keyword(s):  
Exact Solution ◽  
Spectroscopic Data ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Curve Matching ◽  
Practical Applications ◽  
Approximation Quality ◽  
Real World Applications ◽  
Polygonal Curves

We study a modified version of the partial Fréchet similarity that is motivated by real world applications, e.g. the analysis of spectroscopic data in the context of astroinformatics and the analysis of birds’ migration trajectories. In those practical applications of curve matching it is often necessary to ignore outliers while dissimilarities regarding individual directions should be weighted by individual costs. We enable both by computing the partial Fréchet similarity between polygonal curves w.r.t. a non-uniform metric. In particular, we measure distances by a function [Formula: see text] that is induced by a set of weighted vectors. We discuss the approximation quality of [Formula: see text] regarding any [Formula: see text] metric and present a polynomial time algorithm for computing an exact solution of the resulting modified partial Fréchet similarity.

COMPUTATIONAL COMPLEXITY OF THE PERFECT MATCHING PROBLEM IN HYPERGRAPHS WITH SUBCRITICAL DENSITY

2010 ◽  
Vol 21 (06) ◽  
pp. 905-924 ◽  
Author(s):  
MAREK KARPIŃSKI ◽  
ANDRZEJ RUCIŃSKI ◽  
EDYTA SZYMAŃSKA
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Perfect Matching ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Existence Problem ◽  
Matching Problem ◽  
Uniform Hypergraphs ◽  
The Status ◽  
Np Complete

In this paper we consider the computational complexity of deciding the existence of a perfect matching in certain classes of dense k-uniform hypergraphs. It has been known that the perfect matching problem for the classes of hypergraphs H with minimum ((k - 1)–wise) vertex degreeδ(H) at least c|V(H)| is NP-complete for [Formula: see text] and trivial for c ≥ ½, leaving the status of the problem with c in the interval [Formula: see text] widely open. In this paper we show, somehow surprisingly, that ½ is not the threshold for tractability of the perfect matching problem, and prove the existence of an ε > 0 such that the perfect matching problem for the class of hypergraphs H with δ(H) ≥ (½ - ε)|V(H)| is solvable in polynomial time. This seems to be the first polynomial time algorithm for the perfect matching problem on hypergraphs for which the existence problem is nontrivial. In addition, we consider parallel complexity of the problem, which could be also of independent interest.

scholarly journals An Edmonds-Gallai-Type Decomposition for the j-Restricted k-Matching Problem

10.37236/7837 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Yanjun Li ◽  
Jácint Szabó
Keyword(s):  
Positive Integer ◽  
Undirected Graph ◽  
Decomposition Theorem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Alternative Proof ◽  
Connected Components ◽  
Matching Problem ◽  
Np Hardness ◽  
Type Decomposition

Given a non-negative integer $j$ and a positive integer $k$, a $j$-restricted $k$-matching in a simple undirected graph is a $k$-matching, so that each of its connected components has at least $j+1$ edges. The maximum non-negative node weighted $j$-restricted $k$-matching problem was recently studied by Li who gave a polynomial-time algorithm and a min-max theorem for $0 \leqslant j < k$, and also proved the NP-hardness of the problem with unit node weights and $2 \leqslant k \leqslant j$. In this paper we derive an Edmonds–Gallai-type decomposition theorem for the $j$-restricted $k$-matching problem with $0 \leqslant j < k$, using the analogous decomposition for $k$-piece packings given by Janata, Loebl and Szabó, and give an alternative proof to the min-max theorem of Li.

scholarly journals Computational Aspects of Nearly Single-Peaked Electorates

2017 ◽  
Vol 58 ◽  
pp. 297-337 ◽  
Author(s):  
Gábor Erdélyi ◽  
Martin Lackner ◽  
Andreas Pfandler
Keyword(s):  
Polynomial Time ◽  
Strategic Behavior ◽  
Distance Measure ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Distance Measures ◽  
Voting Rules ◽  
Single Peakedness ◽  
Computational Aspects ◽  
And Control

Manipulation, bribery, and control are well-studied ways of changing the outcome of an election. Many voting rules are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to single-peaked electorates, these rules suddenly become easy to manipulate. Recently, Faliszewski, Hemaspaandra, and Hemaspaandra studied the computational complexity of strategic behavior in nearly single-peaked electorates. These are electorates that are not single-peaked but close to it according to some distance measure. In this paper we introduce several new distance measures regarding single-peakedness. We prove that determining whether a given profile is nearly single-peaked is NP-complete in many cases. For one case we present a polynomial-time algorithm. In case the single-peaked axis is given, we show that determining the distance is always possible in polynomial time. Furthermore, we explore the relations between the new notions introduced in this paper and existing notions from the literature.

scholarly journals Heuristics for Hierarchical Partitioning with Application to Model Checking

2000 ◽  
Vol 7 (21) ◽  
Author(s):  
M. Oliver Möller ◽  
Rajeev Alur
Keyword(s):  
Model Checking ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Connected Components ◽  
Opinion Poll ◽  
Low Degree ◽  
Np Complete ◽  
Leader Election Algorithm ◽  
Recent Version

Given a collection of connected components, it is often desired to cluster together<br />parts of strong correspondence, yielding a hierarchical structure. We address the <br />automation of this process and apply heuristics to battle the combinatorial and <br />computational complexity.<br />We define a cost function that captures the quality of a structure relative to the<br />connections and favors shallow structures with a low degree of branching. Finding<br />a structure with minimal cost is shown to be NP-complete. We present a greedy<br />polynomial-time algorithm that creates an approximate good solution incrementally<br />by local evaluation of a heuristic function. We compare some simple heuristic <br />functions and argue for one based on four criteria: The number of enclosed connections,<br />the number of components, the number of touched connections and the depth of the structure.<br />We report on an application in the context of formal verication, where our <br />algorithm serves as a preprocessor for a temporal scaling technique, called \"ext" heuristic<br /> [AW99]. The latter is applicable in enumerative reachability analysis and is included<br />in the recent version of the Mocha model checking tool.<br />We demonstrate performance and benefits of our method and use an asynchronous<br />parity computer, a standard leader election algorithm, and an opinion poll protocol as<br />case studies.

scholarly journals Partners in Crime: Manipulating the Deferred Acceptance Algorithm through an Accomplice

2019 ◽  
Vol 33 ◽  
pp. 9917-9918
Author(s):  
Theodora Bendlin ◽  
Hadi Hosseini
Keyword(s):  
Stable Matching ◽  
Single Woman ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
The Stability ◽  
Manipulation Strategy

We introduce a new manipulation strategy available to women in the men-proposing stable matching, called manipulation through an accomplice. In this strategy, a woman can team up with a potential male “accomplice” who manipulates on her behalf to obtain a better match for her. We investigate the stability of the matching obtained after this manipulation, provide an algorithm to compute such strategies, and show its benefit compared to single-woman manipulation strategies.

scholarly journals An Algorithmic Friedman–Pippenger Theorem on Tree Embeddings and Applications

10.37236/851 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Domingos Dellamonica Jr ◽  
Yoshiharu Kohayakawa
Keyword(s):  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Expander Graphs ◽  
Small Tree ◽  
Matching Problem ◽  
Bounded Degree ◽  
Algorithmic Approach ◽  
Alternative Result ◽  
On Line ◽  
Bounded Degree Trees

An $(n, d)$-expander is a graph $G = (V, E)$ such that for every $X \subseteq V$ with $|X| \leq 2n - 2$ we have $|\Gamma_G(X)| \geq (d+1)|X|$. A tree $T$ is small if it has at most $n$ vertices and has maximum degree at most $d$. Friedman and Pippenger (1987) proved that any $(n, d)$-expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs $G$ of $(N,D,\lambda)$-graphs $\Lambda$, as long as $G$ contains a positive fraction of the edges of $\Lambda$ and $\lambda/D$ is small enough. In several applications of the Friedman–Pippenger theorem, including the ones in the original paper of those authors, the $(n,d)$-expander $G$ is a subgraph of an $(N,D,\lambda)$-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman–Pippenger theorem. We shall also show a construction inspired on Wigderson–Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

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