scholarly journals Multi-dimensional Rankings, Program Termination, and Complexity Bounds of Flowchart Programs

2010 ◽  
pp. 117-133 ◽  
Author(s):  
Christophe Alias ◽  
Alain Darte ◽  
Paul Feautrier ◽  
Laure Gonnord
Keyword(s):  
Complexity Bounds ◽  
Program Termination

Approximate Mining of Frequent -Subgraph Patterns in Evolving Graphs

2021 ◽  
Vol 15 (3) ◽  
pp. 1-35
Author(s):  
Muhammad Anis Uddin Nasir ◽  
Cigdem Aslay ◽  
Gianmarco De Francisci Morales ◽  
Matteo Riondato
Keyword(s):  
Sample Size ◽  
State Of The Art ◽  
Empirical Evaluation ◽  
Connected Subgraph ◽  
Dynamic Graphs ◽  
High Quality ◽  
Complexity Bounds ◽  
Approximation Quality ◽  
Uniform Sample ◽  
Waiting For Godot

“Perhaps he could dance first and think afterwards, if it isn’t too much to ask him.” S. Beckett, Waiting for Godot Given a labeled graph, the collection of -vertex induced connected subgraph patterns that appear in the graph more frequently than a user-specified minimum threshold provides a compact summary of the characteristics of the graph, and finds applications ranging from biology to network science. However, finding these patterns is challenging, even more so for dynamic graphs that evolve over time, due to the streaming nature of the input and the exponential time complexity of the problem. We study this task in both incremental and fully-dynamic streaming settings, where arbitrary edges can be added or removed from the graph. We present TipTap , a suite of algorithms to compute high-quality approximations of the frequent -vertex subgraphs w.r.t. a given threshold, at any time (i.e., point of the stream), with high probability. In contrast to existing state-of-the-art solutions that require iterating over the entire set of subgraphs in the vicinity of the updated edge, TipTap operates by efficiently maintaining a uniform sample of connected -vertex subgraphs, thanks to an optimized neighborhood-exploration procedure. We provide a theoretical analysis of the proposed algorithms in terms of their unbiasedness and of the sample size needed to obtain a desired approximation quality. Our analysis relies on sample-complexity bounds that use Vapnik–Chervonenkis dimension, a key concept from statistical learning theory, which allows us to derive a sufficient sample size that is independent from the size of the graph. The results of our empirical evaluation demonstrates that TipTap returns high-quality results more efficiently and accurately than existing baselines.

scholarly journals Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials

2021 ◽  
Author(s):  
Mareike Dressler ◽  
Adam Kurpisz ◽  
Timo de Wolff
Keyword(s):  
Computer Science ◽  
Affine Transformation ◽  
Optimization Problems ◽  
Polynomial Optimization ◽  
Theoretical Computer Science ◽  
Sums Of Squares ◽  
Theoretical Computer ◽  
Complexity Bounds ◽  
Polynomial Optimization Problems ◽  
Transformation Of Variables

AbstractVarious key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems is based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization problems over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS-based certificates remain valid: First, for polynomials, which are nonnegative over the n-variate boolean hypercube with constraints of degree d there exists a SONC certificate of degree at most $$n+d$$ n + d . Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate that includes at most $$n^{O(d)}$$ n O ( d ) nonnegative circuit polynomials. Moreover, we prove that, in opposite to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar’s Positivstellensatz for SOS. We discuss these results from both the algebraic and the optimization perspective.

The size-change principle for program termination

2001 ◽  
Vol 36 (3) ◽  
pp. 81-92 ◽  
Author(s):  
Chin Soon Lee ◽  
Neil D. Jones ◽  
Amir M. Ben-Amram
Keyword(s):  
Size Change ◽  
Program Termination

Proving program termination

2011 ◽  
Vol 54 (5) ◽  
pp. 88-98 ◽  
Author(s):  
Byron Cook ◽  
Andreas Podelski ◽  
Andrey Rybalchenko
Keyword(s):  
Program Termination

Community Kids Wraparound Mental Health Program: An Effective Approach to Working with Families in Crisis

2007 ◽  
Vol 1 (2) ◽  
pp. 77-99
Author(s):  
Douglas Klayman ◽  
Jenny Crawford
Keyword(s):  
Mental Health ◽  
Experimental Research ◽  
Program Implementation ◽  
Health Program ◽  
Impact Analysis ◽  
Systems Of Care ◽  
Mental Health Program ◽  
Program Termination ◽  
Quasi Experimental ◽  
The Impact

This article presents findings from the five-year evaluation of a youth wraparound mental health program called Community Kids. The structure of the program, sociological theories underlying the philosophy of wraparound, and the context of the mental health system prior to program implementation are discussed. Included are utilization trends from inception through program termination. The impact analysis is presented in terms of five outcome domains for three participant cohorts, defined by tenure in the program. This longitudinal quasi-experimental research provides additional evidence of the efficacy of systems of care and the wraparound model in terms of improving clinical outcomes for youth.

scholarly journals Improved Complexity Bounds for Counting Points on Hyperelliptic Curves

2018 ◽  
Vol 19 (3) ◽  
pp. 591-621 ◽  
Author(s):  
Simon Abelard ◽  
Pierrick Gaudry ◽  
Pierre-Jean Spaenlehauer
Keyword(s):  
Hyperelliptic Curves ◽  
Complexity Bounds ◽  
Counting Points
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