7 research outputs found
Dynamic Dictionary with Subconstant Wasted Bits per Key
Dictionaries have been one of the central questions in data structures. A
dictionary data structure maintains a set of key-value pairs under insertions
and deletions such that given a query key, the data structure efficiently
returns its value. The state-of-the-art dictionaries [Bender, Farach-Colton,
Kuszmaul, Kuszmaul, Liu 2022] store key-value pairs with only bits of redundancy, and support all operations in time,
for . It was recently shown to be optimal [Li, Liang, Yu, Zhou
2023b].
In this paper, we study the regime where the redundant bits is , and
show that when is at least , all operations can be
supported in time, matching the lower bound in this
regime [Li, Liang, Yu, Zhou 2023b]. We present two data structures based on
which range is in. The data structure for utilizes a
generalization of adapters studied in [Berger, Kuszmaul, Polak, Tidor, Wein
2022] and [Li, Liang, Yu, Zhou 2023a]. The data structure for is based on recursively hashing into buckets with logarithmic
sizes.Comment: 46 pages; SODA 202
Dynamic "Succincter"
Augmented B-trees (aB-trees) are a broad class of data structures. The
seminal work "succincter" by Patrascu showed that any aB-tree can be stored
using only two bits of redundancy, while supporting queries to the tree in time
proportional to its depth. It has been a versatile building block for
constructing succinct data structures, including rank/select data structures,
dictionaries, locally decodable arithmetic coding, storing balanced
parenthesis, etc.
In this paper, we show how to "dynamize" an aB-tree. Our main result is the
design of dynamic aB-trees (daB-trees) with branching factor two using only
three bits of redundancy (with the help of lookup tables that are of negligible
size in applications), while supporting updates and queries in time polynomial
in its depth. As an application, we present a dynamic rank/select data
structure for -bit arrays, also known as a dynamic fully indexable
dictionary (FID). It supports updates and queries in
time, and when the array has ones, the data structure occupies bits. Note that the update and
query times are optimal even without space constraints due to a lower bound by
Fredman and Saks. Prior to our work, no dynamic FID with near-optimal update
and query times and redundancy was known. We further show that a
dynamic sequence supporting insertions, deletions and rank/select queries can
be maintained in (optimal) time and with bits of redundancy.Comment: 33 pages, 1 figure; in FOCS 202
Tight Cell-Probe Lower Bounds for Dynamic Succinct Dictionaries
A dictionary data structure maintains a set of at most keys from the
universe under key insertions and deletions, such that given a query , it returns if is in the set. Some variants also store values
associated to the keys such that given a query , the value associated to
is returned when is in the set.
This fundamental data structure problem has been studied for six decades
since the introduction of hash tables in 1953. A hash table occupies bits of space with constant time per operation in expectation. There has
been a vast literature on improving its time and space usage. The
state-of-the-art dictionary by Bender, Farach-Colton, Kuszmaul, Kuszmaul and
Liu [BFCK+22] has space consumption close to the information-theoretic optimum,
using a total of bits, while supporting all operations in
time, for any parameter . The term is referred to as the wasted bits per key.
In this paper, we prove a matching cell-probe lower bound: For
, any dictionary with wasted bits per key
must have expected operational time , in the cell-probe model with
word-size . Furthermore, if a dictionary stores values of
bits, we show that regardless of the query time, it must have
expected update time. It is worth noting that this is the first
cell-probe lower bound on the trade-off between space and update time for
general data structures.Comment: 35 page
On the Perturbation Function of Ranking and Balance for Weighted Online Bipartite Matching
Ranking and Balance are arguably the two most important algorithms in the online matching literature. They achieve the same optimal competitive ratio of 1-1/e for the integral version and fractional version of online bipartite matching by Karp, Vazirani, and Vazirani (STOC 1990) respectively. The two algorithms have been generalized to weighted online bipartite matching problems, including vertex-weighted online bipartite matching and AdWords, by utilizing a perturbation function. The canonical choice of the perturbation function is f(x) = 1-e^{x-1} as it leads to the optimal competitive ratio of 1-1/e in both settings.
We advance the understanding of the weighted generalizations of Ranking and Balance in this paper, with a focus on studying the effect of different perturbation functions. First, we prove that the canonical perturbation function is the unique optimal perturbation function for vertex-weighted online bipartite matching. In stark contrast, all perturbation functions achieve the optimal competitive ratio of 1-1/e in the unweighted setting. Second, we prove that the generalization of Ranking to AdWords with unknown budgets using the canonical perturbation function is at most 0.624 competitive, refuting a conjecture of Vazirani (2021). More generally, as an application of the first result, we prove that no perturbation function leads to the prominent competitive ratio of 1-1/e by establishing an upper bound of 1-1/e-0.0003. Finally, we propose the online budget-additive welfare maximization problem that is intermediate between AdWords and AdWords with unknown budgets, and we design an optimal 1-1/e competitive algorithm by generalizing Balance
On the Perturbation Function of Ranking and Balance for Weighted Online Bipartite Matching
Ranking and Balance are arguably the two most important algorithms in the
online matching literature. They achieve the same optimal competitive ratio of
for the integral version and fractional version of online bipartite
matching by Karp, Vazirani, and Vazirani (STOC 1990) respectively. The two
algorithms have been generalized to weighted online bipartite matching
problems, including vertex-weighted online bipartite matching and AdWords, by
utilizing a perturbation function. The canonical choice of the perturbation
function is as it leads to the optimal competitive ratio of
in both settings.
We advance the understanding of the weighted generalizations of Ranking and
Balance in this paper, with a focus on studying the effect of different
perturbation functions. First, we prove that the canonical perturbation
function is the \emph{unique} optimal perturbation function for vertex-weighted
online bipartite matching. In stark contrast, all perturbation functions
achieve the optimal competitive ratio of in the unweighted setting.
Second, we prove that the generalization of Ranking to AdWords with unknown
budgets using the canonical perturbation function is at most
competitive, refuting a conjecture of Vazirani (2021). More generally, as an
application of the first result, we prove that no perturbation function leads
to the prominent competitive ratio of by establishing an upper bound of
.
Finally, we propose the online budget-additive welfare maximization problem
that is intermediate between AdWords and AdWords with unknown budgets, and we
design an optimal competitive algorithm by generalizing Balance.Comment: Conference version to appear at the European Symposium on Algorithms
(ESA 2023). 16 pages, 2 figures, 8 pages appendi
Clinicopathological and prognostic significance of chemokine receptor CXCR4 overexpression in patients with esophageal cancer: a meta-analysis
The prognostic significance of CXC chemokine receptor type 4 (CXCR4) for survival of patients with esophageal cancer remains controversial. To investigate its expression impact on clinicopathological features and survival outcome, a meta-analysis was performed. A comprehensive search in the PubMed, Embase, and Web of Science (up to October 8, 2013) was performed for relevant studies using multiple search strategies. Correlation between CXCR4 expression and clinicopathological features and overall survival (OS) was analyzed. A total of 1,055 patients with esophageal cancer from seven studies were included. The pooled odds ratios (ORs) which indicated CXCR4 expression was associated with tumor depth (OR = 0.35, confidence interval (CI) = 0.27-0.47, P < 0.00001), status of lymph node (OR = 0.36, CI = 0.21-0.61, P < 0.0002), TNM (tumor, node, metastasis) stage (OR = 0.38, CI = 0.25-0.56, P < 0.00001), and histological type (OR = 1.81, CI = 1.07-3.05, P = 0.03). Poor overall survival of esophageal cancer was found to be significantly related to CXCR4 overexpression (hazard ratio (HR) 1.49, 95 % CI = 1.24-1.80, P < 0.0001), whereas combined ORs exhibited that CXCR4 expression has no correlation with gender or tumor differentiation. Based on the published studies, CXCR4 overexpression in patients with esophageal cancer indicated worse survival outcome and was associated with common clinicopathological poor prognostic factors
Fluid‐Driven High‐Performance Bionic Artificial Muscle with Adjustable Muscle Architecture
High‐performance artificial muscle is always the pursuit of researchers for robotics. Herein, a bionic artificial muscle is reported called “ExoMuscle” mimicking the sarcomere in skeletal muscle with a bio‐inspired structure to contract “myofilaments” enabling the artificial muscle to mimic the architecture of muscle such as parallel, fusiform, convergent, and pennation and beyond the performance of skeletal muscle. The reported actuators excel in various aspects compared with skeletal muscle including actuation stress (0.41–0.9 MPa), strain (50%), optimal length, velocity‐independence output, power density (10.94 kW kg−1), and efficiency (69.11%). With its own adjustable pennation architecture, it achieves variable actuation stress up to 0.9 MPa meanwhile maintaining high efficiency. Furthermore, ExoMuscle highly conforms to the anatomical complexity of the human body to cooperate with skeletal muscles closely opening the door for bio‐robotics, especially wearable robots