61 research outputs found
Formal Methods: From Academia to Industrial Practice. A Travel Guide
For many decades, formal methods are considered to be the way forward to help
the software industry to make more reliable and trustworthy software. However,
despite this strong belief and many individual success stories, no real change
in industrial software development seems to be occurring. In fact, the software
industry itself is moving forward rapidly, and the gap between what formal
methods can achieve and the daily software-development practice does not appear
to be getting smaller (and might even be growing).
In the past, many recommendations have already been made on how to develop
formal-methods research in order to close this gap. This paper investigates why
the gap nevertheless still exists and provides its own recommendations on what
can be done by the formal-methods-research community to bridge it. Our
recommendations do not focus on open research questions. In fact,
formal-methods tools and techniques are already of high quality and can address
many non-trivial problems; we do give some technical recommendations on how
tools and techniques can be made more accessible. To a greater extent, we focus
on the human aspect: how to achieve impact, how to change the way of thinking
of the various stakeholders about this issue, and in particular, as a research
community, how to alter our behaviour, and instead of competing, collaborate to
address this issue.Comment: 22 pages, 0 figure
Dynamic Graph Stream Algorithms in Space
In this paper we study graph problems in dynamic streaming model, where the
input is defined by a sequence of edge insertions and deletions. As many
natural problems require space, where is the number of
vertices, existing works mainly focused on designing space
algorithms. Although sublinear in the number of edges for dense graphs, it
could still be too large for many applications (e.g. is huge or the graph
is sparse). In this work, we give single-pass algorithms beating this space
barrier for two classes of problems.
We present space algorithms for estimating the number of connected
components with additive error and
-approximating the weight of minimum spanning tree, for any
small constant . The latter improves previous
space algorithm given by Ahn et al. (SODA 2012) for connected graphs with
bounded edge weights.
We initiate the study of approximate graph property testing in the dynamic
streaming model, where we want to distinguish graphs satisfying the property
from graphs that are -far from having the property. We consider
the problem of testing -edge connectivity, -vertex connectivity,
cycle-freeness and bipartiteness (of planar graphs), for which, we provide
algorithms using roughly space, which is
for any constant .
To complement our algorithms, we present space
lower bounds for these problems, which show that such a dependence on
is necessary.Comment: ICALP 201
Low Diameter Graph Decompositions by Approximate Distance Computation
In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the probability that an edge is cut by the decomposition scales linearly with the length of the edge. There is a large body of literature on low diameter graph decomposition with small edge cutting probabilities, with all existing techniques heavily building on single source shortest paths (SSSP) computations. Unfortunately, in many theoretical models for large-scale computations, the SSSP task constitutes a complexity bottleneck. Therefore, it is desirable to replace exact SSSP computations with approximate ones. However this imposes a fundamental challenge since the existing constructions of low diameter graph decomposition with small edge cutting probabilities inherently rely on the subtractive form of the triangle inequality, which fails to hold under distance approximation.
The current paper overcomes this obstacle by developing a technique termed blurry ball growing. By combining this technique with a clever algorithmic idea of Miller et al. (SPAA 2013), we obtain a construction of low diameter decompositions with small edge cutting probabilities which replaces exact SSSP computations by (a small number of) approximate ones. The utility of our approach is showcased by deriving efficient algorithms that work in the CONGEST, PRAM, and semi-streaming models of computation. As an application, we obtain metric tree embedding algorithms in the vein of Bartal (FOCS 1996) whose computational complexities in these models are optimal up to polylogarithmic factors. Our embeddings have the additional useful property that the tree can be mapped back to the original graph such that each edge is "used" only logaritmically many times, which is of interest for capacitated problems and simulating CONGEST algorithms on the tree into which the graph is embedded
Tight Regret Bounds for Single-pass Streaming Multi-armed Bandits
Regret minimization in streaming multi-armed bandits (MABs) has been studied
extensively in recent years. In the single-pass setting with arms and
trials, a regret lower bound of has been proved for any
algorithm with memory (Maiti et al. [NeurIPS'21]; Agarwal at al.
[COLT'22]). On the other hand, however, the previous best regret upper bound is
still , which is achieved by the streaming
implementation of the simple uniform exploration. The
gap leaves the open question of the tight regret bound in the single-pass MABs
with sublinear arm memory.
In this paper, we answer this open problem and complete the picture of regret
minimization in single-pass streaming MABs. We first improve the regret lower
bound to for algorithms with memory, which
matches the uniform exploration regret up to a logarithm factor in . We then
show that the factor is not necessary, and we can achieve
regret by finding an -best arm and committing
to it in the rest of the trials. For regret minimization with high constant
probability, we can apply the single-memory -best arm algorithms
in Jin et al. [ICML'21] to obtain the optimal bound. Furthermore, for the
expected regret minimization, we design an algorithm with a single-arm memory
that achieves regret, and an algorithm with
-memory with the optimal regret following
the -best arm algorithm in Assadi and Wang [STOC'20].
We further tested the empirical performances of our algorithms. The
simulation results show that the proposed algorithms consistently outperform
the benchmark uniform exploration algorithm by a large margin, and on occasion,
reduce the regret by up to 70%.Comment: ICML 202
Near-Quadratic Lower Bounds for Two-Pass Graph Streaming Algorithms
We prove that any two-pass graph streaming algorithm for the -
reachability problem in -vertex directed graphs requires near-quadratic
space of bits. As a corollary, we also obtain near-quadratic space
lower bounds for several other fundamental problems including maximum bipartite
matching and (approximate) shortest path in undirected graphs.
Our results collectively imply that a wide range of graph problems admit
essentially no non-trivial streaming algorithm even when two passes over the
input is allowed. Prior to our work, such impossibility results were only known
for single-pass streaming algorithms, and the best two-pass lower bounds only
ruled out space algorithms, leaving open a large gap between
(trivial) upper bounds and lower bounds
- …