22 research outputs found
Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality
We consider the all pairs all shortest paths (APASP) problem, which maintains
the shortest path dag rooted at every vertex in a directed graph G=(V,E) with
positive edge weights. For this problem we present a decremental algorithm
(that supports the deletion of a vertex, or weight increases on edges incident
to a vertex). Our algorithm runs in amortized O(\vstar^2 \cdot \log n) time per
update, where n=|V|, and \vstar bounds the number of edges that lie on shortest
paths through any given vertex. Our APASP algorithm can be used for the
decremental computation of betweenness centrality (BC), a graph parameter that
is widely used in the analysis of large complex networks. No nontrivial
decremental algorithm for either problem was known prior to our work. Our
method is a generalization of the decremental algorithm of Demetrescu and
Italiano [DI04] for unique shortest paths, and for graphs with \vstar =O(n), we
match the bound in [DI04]. Thus for graphs with a constant number of shortest
paths between any pair of vertices, our algorithm maintains APASP and BC scores
in amortized time O(n^2 \log n) under decremental updates, regardless of the
number of edges in the graph.Comment: An extended abstract of this paper will appear in Proc. ISAAC 201
Fully-dynamic Approximation of Betweenness Centrality
Betweenness is a well-known centrality measure that ranks the nodes of a
network according to their participation in shortest paths. Since an exact
computation is prohibitive in large networks, several approximation algorithms
have been proposed. Besides that, recent years have seen the publication of
dynamic algorithms for efficient recomputation of betweenness in evolving
networks. In previous work we proposed the first semi-dynamic algorithms that
recompute an approximation of betweenness in connected graphs after batches of
edge insertions.
In this paper we propose the first fully-dynamic approximation algorithms
(for weighted and unweighted undirected graphs that need not to be connected)
with a provable guarantee on the maximum approximation error. The transfer to
fully-dynamic and disconnected graphs implies additional algorithmic problems
that could be of independent interest. In particular, we propose a new upper
bound on the vertex diameter for weighted undirected graphs. For both weighted
and unweighted graphs, we also propose the first fully-dynamic algorithms that
keep track of such upper bound. In addition, we extend our former algorithm for
semi-dynamic BFS to batches of both edge insertions and deletions.
Using approximation, our algorithms are the first to make in-memory
computation of betweenness in fully-dynamic networks with millions of edges
feasible. Our experiments show that they can achieve substantial speedups
compared to recomputation, up to several orders of magnitude
How Good Are Popular Matchings?
In this paper, we consider the Hospital Residents problem (HR) and the Hospital Residents problem with Lower Quotas (HRLQ). In this model with two sided preferences, stability is a well accepted notion of optimality. However, in the presence of lower quotas, a stable and feasible matching need not exist. For the HRLQ problem, our goal therefore is to output a good feasible matching assuming that a feasible matching exists. Computing matchings with minimum number of blocking pairs (Min-BP) and minimum number of blocking residents (Min-BR) are known to be NP-Complete. The only approximation algorithms for these problems work under severe restrictions on the preference lists. We present an algorithm which circumvents this restriction and computes a popular matching in the HRLQ instance. We show that on data-sets generated using various generators, our algorithm performs very well in terms of blocking pairs and blocking residents. Yokoi [Yokoi, 2017] recently studied envy-free matchings for the HRLQ problem. We propose a simple modification to Yokoi\u27s algorithm to output a maximal envy-free matching. We observe that popular matchings outperform envy-free matchings on several parameters of practical importance, like size, number of blocking pairs, number of blocking residents.
In the absence of lower quotas, that is, in the Hospital Residents (HR) problem, stable matchings are guaranteed to exist. Even in this case, we show that popularity is a practical alternative to stability. For instance, on synthetic data-sets generated using a particular model, as well as on real world data-sets, a popular matching is on an average 8-10% larger in size, matches more number of residents to their top-choice, and more residents prefer the popular matching as compared to a stable matching. Our comprehensive study reveals the practical appeal of popular matchings for the HR and HRLQ problems. To the best of our knowledge, this is the first study on the empirical evaluation of popular matchings in this setting
Code Generation for a Variety of Accelerators for a Graph DSL
Sparse graphs are ubiquitous in real and virtual worlds. With the phenomenal
growth in semi-structured and unstructured data, sizes of the underlying graphs
have witnessed a rapid growth over the years. Analyzing such large structures
necessitates parallel processing, which is challenged by the intrinsic
irregularity of sparse computation, memory access, and communication. It would
be ideal if programmers and domain-experts get to focus only on the sequential
computation and a compiler takes care of auto-generating the parallel code. On
the other side, there is a variety in the number of target hardware devices,
and achieving optimal performance often demands coding in specific languages or
frameworks. Our goal in this work is to focus on a graph DSL which allows the
domain-experts to write almost-sequential code, and generate parallel code for
different accelerators from the same algorithmic specification. In particular,
we illustrate code generation from the StarPlat graph DSL for NVIDIA, AMD, and
Intel GPUs using CUDA, OpenCL, SYCL, and OpenACC programming languages. Using a
suite of ten large graphs and four popular algorithms, we present the efficacy
of StarPlat's versatile code generator.Comment: arXiv admin note: text overlap with arXiv:2305.0331
Manipulation Strategies for the Rank Maximal Matching Problem
We consider manipulation strategies for the rank-maximal matching problem. In
the rank-maximal matching problem we are given a bipartite graph such that denotes a set of applicants and a set of posts. Each
applicant has a preference list over the set of his neighbours in
, possibly involving ties. Preference lists are represented by ranks on the
edges - an edge has rank , denoted as , if post
belongs to one of 's -th choices. A rank-maximal matching is one in which
the maximum number of applicants is matched to their rank one posts and subject
to this condition, the maximum number of applicants is matched to their rank
two posts, and so on. A rank-maximal matching can be computed in time, where denotes the number of applicants, the
number of edges and the maximum rank of an edge in an optimal solution.
A central authority matches applicants to posts. It does so using one of the
rank-maximal matchings. Since there may be more than one rank- maximal matching
of , we assume that the central authority chooses any one of them randomly.
Let be a manipulative applicant, who knows the preference lists of all
the other applicants and wants to falsify his preference list so that he has a
chance of getting better posts than if he were truthful. In the first problem
addressed in this paper the manipulative applicant wants to ensure that
he is never matched to any post worse than the most preferred among those of
rank greater than one and obtainable when he is truthful. In the second problem
the manipulator wants to construct such a preference list that the worst post
he can become matched to by the central authority is best possible or in other
words, wants to minimize the maximal rank of a post he can become matched
to
Popular Mixed Matchings
AbstractWe study the problem of matching applicants to jobs under one-sided preferences; that is, each applicant ranks a non-empty subset of jobs under an order of preference, possibly involving ties. A matching M is said to be more popular than T if the applicants that prefer M to T outnumber those that prefer T to M. A matching is said to be popular if there is no matching more popular than it. Equivalently, a matching M is popular if ϕ(M,T)≥ϕ(T,M) for all matchings T, where ϕ(X,Y) is the number of applicants that prefer X to Y.Previously studied solution concepts based on the popularity criterion are either not guaranteed to exist for every instance (e.g., popular matchings) or are NP-hard to compute (e.g., least unpopular matchings). This paper addresses this issue by considering mixed matchings. A mixed matching is simply a probability distribution over matchings in the input graph. The function ϕ that compares two matchings generalizes in a natural manner to mixed matchings by taking expectation. A mixed matching P is popular if ϕ(P,Q)≥ϕ(Q,P) for all mixed matchings Q.We show that popular mixed matchings always exist and we design polynomial time algorithms for finding them. Then we study their efficiency and give tight bounds on the price of anarchy and price of stability of the popular matching problem
Blood lipid metabolites and meat lipid peroxidation responses of broiler chickens to dietary lecithinized palm oil
This trial was conducted to investigate the effects of supplementing saturated and unsaturated fat sources on serum metabolites and meat physiochemical parameters in the diets of broiler chickens. A total of 360 day-old male broiler chicks (Ross 308) were used in a completely randomized design with five treatments and six replicates of 14 chicks. The assay diets were developed by applying a basal diet with no supplemented fat and the addition of soybean oil (SO), lecithinized palm oil (LPO), a 50 : 50 mix of SO and LPO (ESL), and 75 : 25 mix of SO and LPO (HSL) ratios to the basal diet. The inclusion levels of experimental fats were 2% and 4% in the starter and growing periods, respectively. Blood samples were collected from broilers to evaluate serum biochemical metabolites on day 41. Thigh meat samples were provided and analysed after 1, 5 and 10 days’ storage to evaluate lipid peroxidation at the end of the experiment. Fat and protein contents of thigh muscle and abdominal fat weight were measured and reported. Chickens fed LPO had greater serum triacylglycerol and very low density lipoprotein concentrations compared with those that received other dietary treatments (P <0.05). The fat content of the meat was higher in birds supplemented with SO, LPO and ESL than control (P <0.05). After 5 and 10 days of storage, the values of thiobarbituric acid reactive substance were lower in meat of broilers receiving LPO than SO and HSL (P <0.05). In conclusion, LPO decreased lipid peroxidation during different storage periods compared with SO.Keywords: Blood parameters, broilers, fat type, meat physiochemical parameter