Recognition of Facets for Knapsack Polytope is DP-complete

DP is a complexity class that is the class of all languages that are the intersection of a language in NP and a language in co-NP, as coined by Papadimitriou and Yannakakis. In this paper, we will establish that, recognizing a facet for the knapsack polytope is DP-complete, as conjectured by Hartvigsen and Zemel in 1992. Moreover, we show that the recognition problem of a supporting hyperplane for the knapsack polytope and the exact knapsack problem are both DP-complete, and the membership problem of knapsack polytope is NP-complete

Characterization of the Cutting-plane Closure

We study the equivalent condition for the closure of any particular family of cutting-planes to be polyhedral, from the perspective of convex geometry. We also propose a new concept for valid inequalities of a convex set, namely the finitely-irredundant inequality (FII), and show that a full-dimensional cutting-plane closure is polyhedral, if and only if it has finitely many FIIs. Based on those results we prove one of the problems left in Bodur et al.: the k-aggregation closure of a covering set is a covering polyhedron

Relaxations and Cutting Planes for Linear Programs with Complementarity Constraints

We study relaxations for linear programs with complementarity constraints, especially instances whose complementary pairs of variables are not independent. Our formulation is based on identifying vertex covers of the conflict graph of the instance and generalizes the extended reformulation-linearization technique of Nguyen, Richard, and Tawarmalani to instances with general complementarity conditions between variables. We demonstrate how to obtain strong cutting planes for our formulation from both the stable set polytope and the boolean quadric polytope associated with a complete bipartite graph. Through an extensive computational study for three types of practical problems, we assess the performance of our proposed linear relaxation and new cutting-planes in terms of the optimality gap closed

TAME: Task Agnostic Continual Learning using Multiple Experts

The goal of lifelong learning is to continuously learn from non-stationary distributions, where the non-stationarity is typically imposed by a sequence of distinct tasks. Prior works have mostly considered idealistic settings, where the identity of tasks is known at least at training. In this paper we focus on a fundamentally harder, so-called task-agnostic setting where the task identities are not known and the learning machine needs to infer them from the observations. Our algorithm, which we call TAME (Task-Agnostic continual learning using Multiple Experts), automatically detects the shift in data distributions and switches between task expert networks in an online manner. At training, the strategy for switching between tasks hinges on an extremely simple observation that for each new coming task there occurs a statistically-significant deviation in the value of the loss function that marks the onset of this new task. At inference, the switching between experts is governed by the selector network that forwards the test sample to its relevant expert network. The selector network is trained on a small subset of data drawn uniformly at random. We control the growth of the task expert networks as well as selector network by employing online pruning. Our experimental results show the efficacy of our approach on benchmark continual learning data sets, outperforming the previous task-agnostic methods and even the techniques that admit task identities at both training and testing, while at the same time using a comparable model size

Delay Impact on Stubborn Mining Attack Severity in Imperfect Bitcoin Network

Stubborn mining attack greatly downgrades Bitcoin throughput and also benefits malicious miners (attackers). This paper aims to quantify the impact of block receiving delay on stubborn mining attack severity in imperfect Bitcoin networks. We develop an analytic model and derive formulas of both relative revenue and system throughput, which are applied to study attack severity. Experiment results validate our analysis method and show that imperfect networks favor attackers. The quantitative analysis offers useful insight into stubborn mining attack and then helps the development of countermeasures.Comment: arXiv admin note: text overlap with arXiv:2302.0021

Have media texts become more humorous?

As a research topic, humour has drawn much attention from multiple disciplines including linguistics. Based on Engelthaler & Hills’ (2018) humour scale, this study developed a measure named Humour Index (HMI) to quantify the degree of humour of texts. This measure was applied to examine the diachronic changes in the degree of humour of American newspapers and magazines across a time span of 118 years (1900-2017) with the use of texts from Corpus of Historical American English (COHA). Besides, the study also discussed the contributions of different types of words to the degree of humour in the two genres. The results show significant uptrends in the degree of humour of both newspapers and magazines in the examined period. Moreover, derogatory and offensive words are found to be less frequently used than other categories of words in both genres. This study provides both theoretical and methodological implications for humour studies and claims or hypotheses of previous research, such as infotainment and linguistic positivity bias