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Aleksandar Ilic

Publications and source records attributed to Aleksandar Ilic.

At least 19 recordsLinked to original sources

Endeavor: Efficient PairHMM for Detection of DNA Variants in Genome-Scale Datasets

DNA variant calling represents a key operation in bioinformatics pipelines that aims at identifying genetic variants. Given an evidenced explosion in genomic data availability, there is an urgent need for a high-performant, portable and efficient solution for variant calling, which can further improve our understanding of genomic structure and genetic basis for complex diseases. In its most common formulation, the Pair Hidden Markov Model (PairHMM) algorithm for variant calling stands as the main bottleneck in the pipeline, accounting for up to 70% of the execution time in large-scale genomic datasets. The state-of-the-art approaches for accelerating PairHMM in CPUs and GPUs do not scale to long DNA sequences and only explore very limited anti-diagonal data parallelism, which yields poor performance. In this work, Endeavor is proposed as a new parallelization strategy for PairHMM that redefines its traditional formulation to explore row-level fine-grained parallelism without loss in solution accuracy. Based on this, a novel and portable SIMD-based approach is derived for efficient and high-performance processing of short and long sequences in CPUs and GPUs, leveraging novel levels of parallelism and synchronization to achieve high throughput in sequences up to 100k basepairs for the first time. Evaluation on Intel and AMD CPUs shows that Endeavor outperforms GKL up to 2.14x in peak throughput and GATK HaplotypeCaller by at least 2x in real-world datasets, while NVIDIA and AMD GPUs achieve up to 2.05x speedups in genome-scale datasets when compared to state-of-the-art GPU-based methods.

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Constant Depth Threshold Circuits For Exhaustive Epistasis Detection

The development of large-scale neuromorphic hardware has made practical implementations of threshold gate-based circuits a near-term possibility. The complexity advantages regarding traditional computing classes, as evidenced in the literature, have prompted us to tackle Epistasis Detection, one of the most computationally complex combinatorial problems in bioinformatics. We propose specially designed circuits that calculate the relative frequencies of all dataset combinations in an efficient pipelined fashion, taking advantage of co-located memory and configurable parallelism, obtaining complexity gains. Overall, we obtain the runtime to be bounded by the number of combinations to calculate, without any additional complexity overhead, contrary to classical approaches, using log-linear space. To accomplish this, we propose a data encoding and combination generation strategy using Leaky Integrate and Fire (LIF) neurons, that feeds a constant depth threshold gate population count circuit. Accounting for typical hardware characteristics, such as limited fan-in and variable precisions, we obtain logarithmic depth and log-cubic linear connections, for the population count circuit by composing developed unbounded fan-in constant depth threshold gate circuits to perform population count and binary array sum.

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CARM Tool: Cache-Aware Roofline Model Automatic Benchmarking and Application Analysis

In recent years, HPC systems and CPU architectures as their central components, have become increasingly complex, making application development and optimization quite challenging. In this respect, intuitive performance models like the Cache-aware Roofline Model (CARM) offer effective guidance by providing insights into bottlenecks that limit the application's ability to reach the system's maximum performance. To fully exploit the benefits of CARM optimization guidance for application development, automatic tools for cross-architecture model construction and in-depth application characterization are absolutely essential. Given a plethora of existing CPU architectures, the current landscape of CARM-enabled tools covers either vendor-specific (Intel Advisor), not sufficiently developed (ARM) or simply non-existing (AMD, RISC-V) tools. This is a particular gap that this work intends to close by bringing automatic CARM support to all major CPU architectures and ISAs, i.e., x86 (Intel, AMD), ARM, and RISC-V, by developing assembly microbenchmarks specifically tailored to cover a full performance spectrum of modern CPUs (from scalar to all supported vector ISA extensions) for both computational units and all memory hierarchy levels. Additionally, this work integrates application analysis within the CARM framework using performance counters and dynamic binary instrumentation. Experimental results show that the CARM roofs constructed with the proposed automated framework provide less than a 1% deviation across various tested architectural maximums.

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PRISM: Processing-In-Memory Sparse MTTKRP for Tensor Decomposition Acceleration

Sparse tensors are the most used representation of sparse multidimensional data. Operations that decompose them, selecting their most important features while reducing their dimension, have become prevalent procedures in machine learning. One of the most used tensor decomposition algorithms is the Alternating Least Squares Canonical Polyadic Decomposition (CP-ALS), where the most time-consuming operation is the Sparse Matricized Tensor Times Khatri-Rao Product (spMTTKRP). This operation is strongly memory-bound, making it hard to implement efficiently on general-purpose processors. This work proposes PRISM, the first approach to tackle this operation using Processing-In-Memory (PIM) technology. We extensively characterize different partitioning strategies, number formats, and kernel optimizations that efficiently adapt this operation to UPMEM PIM, which is further boosted by heterogeneous collaboration with the CPU. The experimental results show that the proposed PIM-based and heterogeneous approaches achieve up to 2.37x and 2.64x speedup compared to state-of-the-art CPU implementations, respectively. However, the UPMEM distributed memory system can significantly hinder performance on certain workloads. Nonetheless, the efficiency of resource consumption for this approach, measured by peak performance fraction usage, is significantly higher than for both CPU and GPU.

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TrioSeq: A Novel Approach to Accelerate Triplet Sequence Alignment on GPUs

State-of-the-art multiple sequence alignment (MSA) algorithms are based on progressive approaches that rely on pairwise sequence alignment (PSA) to generate guide trees to align all sequences. Given an evidenced explosion in genomic data availability, research efforts have focused on accelerating PSA on massively-parallel architectures (e.g., GPUs) and specialized hardware (e.g., FPGAs). However, there is increasing evidence that starting from exact 3-way alignments could provide more robust, accurate MSAs, and improve genomic analysis. While the current literature has shown that PSA algorithms can be extended to align sequence triplets, the existent state-of-the-art on hardware acceleration of exact 3-way alignments is still scarce. In particular, current GPU methods are still inefficient due to lacking support for novel hardware features (e.g., cross-thread intrinsics), while being closed-source and vendor-specific. In this paper, TrioSeq is proposed as a fine-grained strategy to efficiently implement 3-way alignments on GPUs, leveraging novel levels of GPU parallelism and synchronization to achieve high throughput in aligning sequence triplets. Evaluation on NVIDIA and AMD GPUs shows that TrioSeq outperforms state-of-the-art GPU progressive methods on 3-way alignment by at least 20% on simulated genomic datasets.

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Unlocking Personalized Healthcare on Modern CPUs/GPUs: Three-way Gene Interaction Study

Developments in Genome-Wide Association Studies have led to the increasing notion that future healthcare techniques will be personalized to the patient, by relying on genetic tests to determine the risk of developing a disease. To this end, the detection of gene interactions that cause complex diseases constitutes an important application. Similarly to many applications in this field, extensive data sets containing genetic information for a series of patients are used (such as Single-Nucleotide Polymorphisms), leading to high computational complexity and memory utilization, thus constituting a major challenge when targeting high-performance execution in modern computing systems. To close this gap, this work proposes several novel approaches for the detection of three-way gene interactions in modern CPUs and GPUs, making use of different optimizations to fully exploit the target architectures. Crucial insights from the Cache-Aware Roofline Model are used to ensure the suitability of the applications to the computing devices. An extensive study of the architectural features of 13 CPU and GPU devices from all main vendors is also presented, allowing to understand the features relevant to obtain high-performance in this bioinformatics domain. To the best of our knowledge, this study is the first to perform such evaluation for epistasis detection. The proposed approaches are able to surpass the performance of state-of-the-art works in the tested platforms, achieving an average speedup of 3.9$\times$ (7.3$\times$ on CPUs and 2.8$\times$ on GPUs) and maximum speedup of 10.6$\times$ on Intel UHD P630 GPU.

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Optimal algorithm for computing Steiner 3-eccentricities of trees

The Steiner $k$-eccentricity of a vertex $v$ of a graph $G$ is the maximum Steiner distance over all $k$-subsets of $V (G)$ which contain $v$. In this note, we design a linear algorithm for computing the Steiner $3$-eccentricities and the connective Steiner $3$-eccentricity index on a tree and thus improving a quadratic algorithm presented in [G. Yu, X. Li, \emph{Connective Steiner 3-eccentricity index and network similarity measure}, Appl. Math. Comput. 386 (2020), 125446.]

cs.DS↗

On conjectures of network distance measures by using graph spectra

In this note we resolve three conjectures from [M. Dehmer, S. Pickl, Y. Shi, G. Yu, \emph{New inequalities for network distance measures by using graph spectra}, Discrete Appl. Math. 252 (2019), 17--27] on the comparison of distance measures based on the graph spectra, by constructing families of counterexamples and using computer search.

math.CO↗

HeTM: Transactional Memory for Heterogeneous Systems

Modern heterogeneous computing architectures, which couple multi-core CPUs with discrete many-core GPUs (or other specialized hardware accelerators), enable unprecedented peak performance and energy efficiency levels. Unfortunately, though, developing applications that can take full advantage of the potential of heterogeneous systems is a notoriously hard task. This work takes a step towards reducing the complexity of programming heterogeneous systems by introducing the abstraction of Heterogeneous Transactional Memory (HeTM). HeTM provides programmers with the illusion of a single memory region, shared among the CPUs and the (discrete) GPU(s) of a heterogeneous system, with support for atomic transactions. Besides introducing the abstract semantics and programming model of HeTM, we present the design and evaluation of a concrete implementation of the proposed abstraction, which we named Speculative HeTM (SHeTM). SHeTM makes use of a novel design that leverages on speculative techniques and aims at hiding the inherently large communication latency between CPUs and discrete GPUs and at minimizing inter-device synchronization overhead. SHeTM is based on a modular and extensible design that allows for easily integrating alternative TM implementations on the CPU's and GPU's sides, which allows the flexibility to adopt, on either side, the TM implementation (e.g., in hardware or software) that best fits the applications' workload and the architectural characteristics of the processing unit. We demonstrate the efficiency of the SHeTM via an extensive quantitative study based both on synthetic benchmarks and on a porting of a popular object caching system.

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Path matrix and path energy of graphs

Given a graph $G$, we associate a path matrix $P$ whose $(i, j)$ entry represents the maximum number of vertex disjoint paths between the vertices $i$ and $j$, with zeros on the main diagonal. In this note, we resolve four conjectures from [M. M. Shikare, P. P. Malavadkar, S. C. Patekar, I. Gutman, \emph{On Path Eigenvalues and Path Energy of Graphs}, MATCH Commun. Math. Comput. Chem. {\bf 79} (2018), 387--398.] on the path energy of graphs and finally present efficient $O(|E| |V|^3)$ algorithm for computing the path matrix used for verifying computational results.

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Counterexamples to conjectures on graph distance measures based on topological indexes

In this paper we disprove three conjectures from [M. Dehmer, F. Emmert-Streib, Y. Shi, Interrelations of graph distance measures based on topological indices, PLoS ONE 9 (2014) e94985] on graph distance measures based on topological indices by providing explicit classes of trees that do not satisfy proposed inequalities. The constructions are based on the families of trees that have the same Wiener index, graph energy or Randic index - but different degree sequences.

math.CO↗

On the variable common due date, minimal tardy jobs bicriteria two-machine flow shop problem with ordered machines

We consider a special case of the ordinary NP-hard two-machine flow shop problem with the objective of determining simultaneously a minimal common due date and the minimal number of tardy jobs. In [S. S. Panwalkar, C. Koulamas, An O(n^2) algorithm for the variable common due date, minimal tardy jobs bicriteria two-machine flow shop problem with ordered machines, European Journal of Operational Research 221 (2012), 7-13.], the authors presented quadratic algorithm for the problem when each job has its smaller processing time on the first machine. In this note, we improve the running time of the algorithm to O(n log n) by efficient implementation using recently introduced modified binary tree data structure.

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A note on 'A New Approach To Compute Wiener Index'

In this note, we discuss the method explained in the recent paper [P. Manuel, I. Rajasingh, B. Rajan, R. Sundara Rajan, A New Approach To Compute Wiener Index, Journal of Computational and Theoretical Nanoscience 10, (2013) 1515-1521.] for computing the Wiener index of special chemical graphs. The method is actually already well-known and equivalent to the 'cut method' introduced in 1995 by Klavzar, Gutman and Mohar, and used in multiple papers for computing various distance based graph invariants.

math.CO↗

Generalizations of Wiener polarity index and terminal Wiener index

In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. We introduce a generalized Wiener polarity index $W_k (G)$ as the number of unordered pairs of vertices ${u, v}$ of $G$ such that the shortest distance $d (u, v)$ between $u$ and $v$ is $k$ (this is actually the $k$-th coefficient in the Wiener polynomial). For $k = 3$, we get standard Wiener polarity index. Furthermore, we generalize the terminal Wiener index $TW_k (G)$ as the sum of distances between all pairs of vertices of degree $k$. For $k = 1$, we get standard terminal Wiener index. In this paper we describe a linear time algorithm for computing these indices for trees and partial cubes, and characterize extremal trees maximizing the generalized Wiener polarity index and generalized terminal Wiener index among all trees of given order $n$.

math.CO↗

Note on the harmonic index of a graph

The harmonic index of a graph $G$ is defined as the sum of weights $\frac{2}{deg(v) + deg(u)}$ of all edges $uv$ of $E (G)$, where $deg (v)$ denotes the degree of a vertex $v$ in $V (G)$. In this note we generalize results of [L. Zhong, The harmonic index on graphs, Appl. Math. Lett. 25 (2012), 561--566] and establish some upper and lower bounds on the harmonic index of $G$.

math.CO↗

New results on the energy of integral circulant graphs

Circulant graphs are an important class of interconnection networks in parallel and distributed computing. Integral circulant graphs play an important role in modeling quantum spin networks supporting the perfect state transfer as well. The integral circulant graph $\ICG_n (D)$ has the vertex set $Z_n = \{0, 1, 2, ..., n - 1\}$ and vertices $a$ and $b$ are adjacent if $\gcd(a-b,n)\in D$, where $D \subseteq \{d : d \mid n,\ 1\leq d<n\}$. These graphs are highly symmetric, have integral spectra and some remarkable properties connecting chemical graph theory and number theory. The energy of a graph was first defined by Gutman, as the sum of the absolute values of the eigenvalues of the adjacency matrix. Recently, there was a vast research for the pairs and families of non-cospectral graphs having equal energies. Following [R. B. Bapat, S. Pati, \textit{Energy of a graph is never an odd integer}, Bull. Kerala Math. Assoc. 1 (2004) 129--132.], we characterize the energy of integral circulant graph modulo 4. Furthermore, we establish some general closed form expressions for the energy of integral circulant graphs and generalize some results from [A. Ili\' c, \textit{The energy of unitary Cayley graphs}, Linear Algebra Appl. 431 (2009), 1881--1889.]. We close the paper by proposing some open problems and characterizing extremal graphs with minimal energy among integral circulant graphs with $n$ vertices, provided $n$ is even.

math.CO↗

On the extremal properties of the average eccentricity

The eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity $ecc (G)$ of a graph $G$ is the mean value of eccentricities of all vertices of $G$. The average eccentricity is deeply connected with a topological descriptor called the eccentric connectivity index, defined as a sum of products of vertex degrees and eccentricities. In this paper we analyze extremal properties of the average eccentricity, introducing two graph transformations that increase or decrease $ecc (G)$. Furthermore, we resolve four conjectures, obtained by the system AutoGraphiX, about the average eccentricity and other graph parameters (the clique number, the Randi\' c index and the independence number), refute one AutoGraphiX conjecture about the average eccentricity and the minimum vertex degree and correct one AutoGraphiX conjecture about the domination number.

math.CO↗

Efficient algorithm for the vertex connectivity of trapezoid graphs

The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing problems in VLSI design and identifying the optimal chain of non-overlapping fragments in bioinformatics. Using modified binary indexed tree data structure, we design an algorithm for calculating the vertex connectivity of trapezoid graph $G$ with time complexity $O (n \log n)$, where $n$ is the number of trapezoids. Furthermore, we establish sufficient and necessary condition for a trapezoid graph $G$ to be bipartite and characterize trees that can be represented as trapezoid graphs.

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