In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Example Input: We study truthful mechanisms for matching and related problems in a partial information<lb>setting, where the agents’ true utilities are hidden, and the algorithm only has access to ordi-<lb>nal preference information. Our model is motivated by the fact that in many settings, agents<lb>cannot express the numerical values of their utility for different outcomes, but are still able<lb>to rank the outcomes in their order of preference. Specifically, we study problems where the<lb>ground truth exists in the form of a weighted graph of agent utilities, but the algorithm can<lb>only elicit the agents’ private information in the form of a preference ordering for each agent<lb>induced by the underlying weights. Against this backdrop, we design truthful algorithms to<lb>approximate the true optimum solution with respect to the hidden weights. Our techniques<lb>yield universally truthful algorithms for a number of graph problems: a 1.76-approximation<lb>algorithm for Max-Weight Matching, 2-approximation algorithm for Max k-matching, a 6-<lb>approximation algorithm for Densest k-subgraph, and a 2-approximation algorithm for Max<lb>Traveling Salesman as long as the hidden weights constitute a metric. We also provide im-<lb>proved approximation algorithms for such problems when the agents are not able to lie about<lb>their preferences. Our results are the first non-trivial truthful approximation algorithms for<lb>these problems, and indicate that in many situations, we can design robust algorithms even<lb>when the agents may lie and only provide ordinal information instead of precise utilities.
Example Output: Truthful Mechanisms for Matching and Clustering in an Ordinal World

Example Input: We consider relative error low rank approximation of tensors with respect to the Frobenius norm. Namely, given an order-q tensor A ∈ R ∏q i=1 ni , output a rank-k tensor B for which ‖A − B‖F ≤ (1 + ) OPT, where OPT = infrank-k A′ ‖A − A‖F . Despite much success on obtaining relative error low rank approximations for matrices, no such results were known for tensors. One structural issue is that there may be no rank-k tensor Ak achieving the above infinum. Another, computational issue, is that an efficient relative error low rank approximation algorithm for tensors would allow one to compute the rank of a tensor, which is NP-hard. We bypass these two issues via (1) bicriteria and (2) parameterized complexity solutions: 1. We give an algorithm which outputs a rank k′ = O((k/ )q−1) tensor B for which ‖A − B‖F ≤ (1+ ) OPT in nnz(A)+n ·poly(k/ ) time in the real RAM model, whenever either Ak exists or OPT > 0. Here nnz(A) denotes the number of non-zero entries in A. If both Ak does not exist and OPT = 0, then B instead satisfies ‖A − B‖F < γ, where γ is any positive, arbitrarily small function of n. 2. We give an algorithm for any δ > 0 which outputs a rank k tensor B for which ‖A−B‖F ≤ (1+ ) OPT and runs in (nnz(A)+n poly(k/ )+exp(k/ )) ·nδ time in the unit cost RAM model, whenever OPT > 2−O(n ) and there is a rank-k tensor B = ∑k i=1 ui ⊗ vi ⊗ wi for which ‖A − B‖F ≤ (1 + /2) OPT and ‖ui‖2, ‖vi‖2, ‖wi‖2 ≤ 2 δ). If OPT ≤ 2−Ω(nδ), then B instead satisfies ‖A−B‖F ≤ 2−Ω(n δ). Our first result is polynomial time, and in fact input sparsity time, in n, k, and 1/ , for any k ≥ 1 and any 0 < < 1, while our second result is fixed parameter tractable in k and 1/ . For outputting a rank-k tensor, or even a bicriteria solution with rank-Ck for a certain constant C > 1, we show a 2 1−o(1)) time lower bound under the Exponential Time Hypothesis. Our results are based on an “iterative existential argument”, and give the first relative error low rank approximations for tensors for a large number of error measures for which nothing was known. In particular, we give the first relative error approximation algorithms on tensors for: column row and tube subset selection, entrywise `p-low rank approximation for 1 ≤ p < 2, low rank approximation with respect to sum of Euclidean norms of faces or tubes, weighted low rank approximation, and low rank approximation in distributed and streaming models. We also obtain several new results for matrices, such as nnz(A)-time CUR decompositions, improving the previous nnz(A) log n-time CUR decompositions, which may be of independent interest. ∗Work done while visiting IBM Almaden, and supported in part by UTCS TAship (CS361 Spring 17 Introduction to Computer Security). †Supported in part by Simons Foundation, and NSF CCF-1617955. ar X iv :1 70 4. 08 24 6v 1 [ cs .D S] 2 6 A pr 2 01 7
Example Output: Relative Error Tensor Low Rank Approximation

Example Input: Knowledge graph embedding aims to embed entities and relations of knowledge graphs into low-dimensional vector spaces. Translating embedding methods regard relations as the translation from head entities to tail entities, which achieve the state-of-the-art results among knowledge graph embedding methods. However, a major limitation of these methods is the time consuming training process, which may take several days or even weeks for large knowledge graphs, and result in great diculty in practical applications. In this paper, we propose an ecient parallel framework for translating embedding methods, called ParTrans-X, which enables the methods to be paralleled without locks by utilizing the distinguished structures of knowledge graphs. Experiments on two datasets with three typical translating embedding methods, i.e., TransE [3], TransH [19], and a more ecient variant TransEAdaGrad [11] validate that ParTrans-X can speed up the training process by more than an order of magnitude.
Example Output:
Eicient Parallel Translating Embedding For Knowledge Graphs