Recognizing and Eliciting Weakly Single Crossing Profiles on Trees

• URL: http://arxiv.org/abs/1611.04175v4
• Date: Thu, 24 Jul 2025 05:38:22 GMT
• Title: Recognizing and Eliciting Weakly Single Crossing Profiles on Trees
• Authors: Palash Dey,
• Abstract summary: We study the weakly single-crossing domain on trees which is a generalization of the well-studied single-crossing domain in social choice theory.<n>We design a time algorithm for recognizing preference profiles which belong to this domain.<n>We then develop an efficient elicitation algorithm for this domain which works even if the preferences can be accessed only sequentially.
• Score: 4.8951183832371
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce and study the weakly single-crossing domain on trees which is a generalization of the well-studied single-crossing domain in social choice theory. We design a polynomial-time algorithm for recognizing preference profiles which belong to this domain. We then develop an efficient elicitation algorithm for this domain which works even if the preferences can be accessed only sequentially and the underlying single-crossing tree structure is not known beforehand. We also prove matching lower bound on the query complexity of our elicitation algorithm when the number of voters is large compared to the number of candidates. We also prove a lower bound of $\Omega(m^2\log n)$ on the number of queries that any algorithm needs to ask to elicit single crossing profile when random queries are allowed. This resolves an open question in an earlier paper and proves optimality of their preference elicitation algorithm when random queries are allowed.

Related papers

• Exact Algorithms and Lower Bounds for Forming Coalitions of Constrained Maximum Size [0.0]
  We study a version of this problem where each team must additionally be of bounded size.<n>Our main contribution is an algorithm that deals efficiently with tree-like structures (bounded emphtreewidth) for small'' teams.
  arXiv  Detail & Related papers  (2025-05-28T14:11:14Z)
• Simple and Provable Scaling Laws for the Test-Time Compute of Large Language Models [70.07661254213181]
  We propose two algorithms that enjoy provable scaling laws for the test-time compute of large language models.<n>One is a two-stage knockout-style algorithm, where each candidate is evaluated by its average win rate against multiple opponents.<n>The other is a two-stage league-style algorithm, where each candidate is evaluated by its average win rate against multiple opponents.
  arXiv  Detail & Related papers  (2024-11-29T05:29:47Z)
• Pathfinding with Lazy Successor Generation [12.02023514105999]
  We study a pathfinding problem where only locations are given, and edges are implicitly defined. Despite its simple structure, this problem becomes non-trivial with a massive number of locations. We propose a novel LaCAS* algorithm, which does not generate successors all at once but gradually generates successors as the search progresses.
  arXiv  Detail & Related papers  (2024-08-27T23:25:25Z)
• Computing Voting Rules with Elicited Incomplete Votes [11.550634521005968]
  We study voting rules that are computable by querying voters about $t m$ candidates. For scoring rules that are computable with limited-sized queries, we give parameterized upper and lower bounds on the number of such queries.
  arXiv  Detail & Related papers  (2024-02-16T22:17:01Z)
• Nearest Neighbour with Bandit Feedback [4.9094025705644695]
  Our algorithm handles the fully adversarial setting in which no assumptions at all are made about the data-generation process. We give generic regret for our algorithm and further analyse them when applied to the bandit problem in euclidean space.
  arXiv  Detail & Related papers  (2023-06-23T20:09:01Z)
• HARRIS: Hybrid Ranking and Regression Forests for Algorithm Selection [75.84584400866254]
  We propose a new algorithm selector leveraging special forests, combining the strengths of both approaches while alleviating their weaknesses. HARRIS' decisions are based on a forest model, whose trees are created based on optimized on a hybrid ranking and regression loss function.
  arXiv  Detail & Related papers  (2022-10-31T14:06:11Z)
• Exact and Approximate Hierarchical Clustering Using A* [51.187990314731344]
  We introduce a new approach based on A* search for clustering. We overcome the prohibitively large search space by combining A* with a novel emphtrellis data structure. We empirically demonstrate that our method achieves substantially higher quality results than baselines for a particle physics use case and other clustering benchmarks.
  arXiv  Detail & Related papers  (2021-04-14T18:15:27Z)
• Towards Optimally Efficient Tree Search with Deep Learning [76.64632985696237]
  This paper investigates the classical integer least-squares problem which estimates signals integer from linear models. The problem is NP-hard and often arises in diverse applications such as signal processing, bioinformatics, communications and machine learning. We propose a general hyper-accelerated tree search (HATS) algorithm by employing a deep neural network to estimate the optimal estimation for the underlying simplified memory-bounded A* algorithm.
  arXiv  Detail & Related papers  (2021-01-07T08:00:02Z)
• Quick Streaming Algorithms for Maximization of Monotone Submodular Functions in Linear Time [16.346069386394703]
  We consider the problem of monotone, submodular over a ground set of size $n$ subject to cardinality constraint $k$. We introduce the first deterministic algorithms with linear time complexity; these algorithms are streaming algorithms. Our single-pass algorithm obtains a constant ratio in $lceil n / c rceil + c$ oracle queries, for any $c ge 1$.
  arXiv  Detail & Related papers  (2020-09-10T16:35:54Z)
• Efficient Computation of Expectations under Spanning Tree Distributions [67.71280539312536]
  We propose unified algorithms for the important cases of first-order expectations and second-order expectations in edge-factored, non-projective spanning-tree models. Our algorithms exploit a fundamental connection between gradients and expectations, which allows us to derive efficient algorithms.
  arXiv  Detail & Related papers  (2020-08-29T14:58:26Z)
• Differentially Private Clustering: Tight Approximation Ratios [57.89473217052714]
  We give efficient differentially private algorithms for basic clustering problems. Our results imply an improved algorithm for the Sample and Aggregate privacy framework. One of the tools used in our 1-Cluster algorithm can be employed to get a faster quantum algorithm for ClosestPair in a moderate number of dimensions.
  arXiv  Detail & Related papers  (2020-08-18T16:22:06Z)
• Learning to Accelerate Heuristic Searching for Large-Scale Maximum Weighted b-Matching Problems in Online Advertising [51.97494906131859]
  Bipartite b-matching is fundamental in algorithm design, and has been widely applied into economic markets, labor markets, etc. Existing exact and approximate algorithms usually fail in such settings due to either requiring intolerable running time or too much computation resource. We propose textttNeuSearcher which leverages the knowledge learned from previously instances to solve new problem instances.
  arXiv  Detail & Related papers  (2020-05-09T02:48:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.