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.

Ex Input:
There are already quite a few tools for solving the Satisfiability Modulo Theories (SMT) problems. In this paper, we present VolCE, a tool for counting the solutions of SMT constraints, or in other words, for computing the volume of the solution space. Its input is essentially a set of Boolean combinations of linear constraints, where the numeric variables are either all integers or all reals, and each variable is bounded. The tool extends SMT solving with integer solution counting and volume computation/estimation for convex polytopes. Effective heuristics are adopted, which enable the tool to deal with high-dimensional problem instances efficiently and accurately.

Ex Output:
A Tool for Computing and Estimating the Volume of the Solution Space of SMT(LA) Constraints


Ex Input:
We propose a novel deep layer cascade (LC) method to improve the accuracy and speed of semantic segmentation. Unlike the conventional model cascade (MC) that is composed of multiple independent models, LC treats a single deep model as a cascade of several sub-models. Earlier sub-models are trained to handle easy and confident regions, and they progressively feed-forward harder regions to the next sub-model for processing. Convolutions are only calculated on these regions to reduce computations. The proposed method possesses several advantages. First, LC classifies most of the easy regions in the shallow stage and makes deeper stage focuses on a few hard regions. Such an adaptive and ‘difficulty-aware’ learning improves segmentation performance. Second, LC accelerates both training and testing of deep network thanks to early decisions in the shallow stage. Third, in comparison to MC, LC is an endto-end trainable framework, allowing joint learning of all sub-models. We evaluate our method on PASCAL VOC and Cityscapes datasets, achieving state-of-the-art performance and fast speed.

Ex Output:
Not All Pixels Are Equal: Difficulty-Aware Semantic Segmentation via Deep Layer Cascade


Ex 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.

Ex Output:

Truthful Mechanisms for Matching and Clustering in an Ordinal World