arXiv subjects

Bora Uçar

Publications and source records attributed to Bora Uçar.

8 recordsLinked to original sources

arXiv2026

An Efficient Newton Algorithm for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence

Nonnegative Matrix Factorization (NMF) is a fundamental tool in unsupervised learning, which approximates a nonnegative matrix by the product of two low-rank nonnegative factors. The Kullback-Leibler (KL) divergence is best suited to measure the data to model discrepancy when the decomposed data sample follows a Poisson distribution, which is the case for count datasets such as term-document matrices or images. Most KL-NMF algorithms in the literature minimize a separable majorant of the loss to find their next iterate. We argue that this method has reached its limits and propose to use instead the second-order Taylor expansion of the loss, leading to a Newton-type method. We minimize this non-separable surrogate by proposing a generalization of the well-known HALS algorithm. This yields an efficient KL-NMF algorithm which provably converges and which competes favorably with state-of-the-art algorithms on a large variety of datasets.

cs.LG↗

arXiv2025

SUperman: Efficient Permanent Computation on GPUs

The permanent is a function, defined for a square matrix, with applications in various domains including quantum computing, statistical physics, complexity theory, combinatorics, and graph theory. Its formula is similar to that of the determinant; however, unlike the determinant, its exact computation is #P-complete, i.e., there is no algorithm to compute the permanent in polynomial time unless P=NP. For an $n \times n$ matrix, the fastest algorithm has a time complexity of $O(2^{n-1}n)$. Although supercomputers have been employed for permanent computation before, there is no work and, more importantly, no publicly available software that leverages cutting-edge High-Performance Computing accelerators such as GPUs. In this work, we design, develop, and investigate the performance of SUperman, a complete software suite that can compute matrix permanents on multiple nodes/GPUs on a cluster while handling various matrix types, e.g., real/complex/binary and sparse/dense, etc., with a unique treatment for each type. SUperman run on a single Nvidia A100 GPU is up to $86\times$ faster than a state-of-the-art parallel algorithm on 44 Intel Xeon cores running at 2.10GHz. Leveraging 192 GPUs, SUperman computes the permanent of a $62 \times 62$ matrix in 1.63 days, marking the largest reported permanent computation to date.

cs.DC↗

arXiv2025

Semi-Streaming Algorithms for Hypergraph Matching

We propose two one-pass streaming algorithms for the $\mathcal{NP}$-hard hypergraph matching problem. The first algorithm stores a small subset of potential matching edges in a stack using dual variables to select edges. It has an approximation guarantee of $\frac{1}{d(1+\varepsilon)}$ and requires $\mathcal{O}((\frac{n}{\varepsilon}) \log^2{n})$ bits of memory, where $n$ is the number of vertices in the hypergraph, $d$ is the maximum number of vertices in a hyperedge, and $ε> 0$ is a parameter to be chosen. The second algorithm computes, stores, and updates a single matching as the edges stream, with an approximation ratio dependent on a parameter $α$. Its best approximation guarantee is $\frac{1}{(2d-1) + 2 \sqrt{d(d-1)}}$, and it requires only $\mathcal{O}(n)$ memory. We have implemented both algorithms and compared them with respect to solution quality, memory consumption, and running times on two diverse sets of hypergraphs with a non-streaming greedy and a naive streaming algorithm. Our results show that the streaming algorithms achieve much better solution quality than naive algorithms when facing adverse orderings. Furthermore, these algorithms reduce the memory required by a factor of 13 in the geometric mean on our test problems, and also outperform the offline Greedy algorithm in running time.

cs.DS↗

arXiv2025

Near-Optimal Minimum Cuts in Hypergraphs at Scale

The hypergraph minimum cut problem aims to partition its vertices into two blocks while minimizing the total weight of the cut hyperedges. This fundamental problem arises in network reliability, VLSI design, and community detection. We present HeiCut, a scalable algorithm for computing near-optimal minimum cuts in both unweighted and weighted hypergraphs. HeiCut aggressively reduces the hypergraph size through a sequence of provably exact reductions that preserve the minimum cut, along with an optional heuristic contraction based on label propagation. It then solves a relaxed Binary Integer Linear Program (BIP) on the reduced hypergraph to compute a near-optimal minimum cut. Our extensive evaluation on over 500 real-world hypergraphs shows that HeiCut computes the exact minimum cut in over 85% of instances using our exact reductions alone, and offers the best solution quality across all instances. It solves over twice as many instances as the state-of-the-art within set computational limits, and is up to five orders of magnitude faster.

cs.DS↗

arXiv2023

Open Problems in (Hyper)Graph Decomposition

Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gain new insights about our surroundings. Even if the final application concerns a different problem (such as traversal, finding paths, trees, and flows), decomposing large graphs is often an important subproblem for complexity reduction or parallelization. This report is a summary of discussions that happened at Dagstuhl seminar 23331 on "Recent Trends in Graph Decomposition" and presents currently open problems and future directions in the area of (hyper)graph decomposition.

cs.DS↗

arXiv2021

Fully-dynamic Weighted Matching Approximation in Practice

Finding large or heavy matchings in graphs is a ubiquitous combinatorial optimization problem. In this paper, we engineer the first non-trivial implementations for approximating the dynamic weighted matching problem. Our first algorithm is based on random walks/paths combined with dynamic programming. The second algorithm has been introduced by Stubbs and Williams without an implementation. Roughly speaking, their algorithm uses dynamic unweighted matching algorithms as a subroutine (within a multilevel approach); this allows us to use previous work on dynamic unweighted matching algorithms as a black box in order to obtain a fully-dynamic weighted matching algorithm. We empirically study the algorithms on an extensive set of dynamic instances and compare them with optimal weighted matchings. Our experiments show that the random walk algorithm typically fares much better than Stubbs/Williams (regarding the time/quality tradeoff), and its results are often not far from the optimum.

cs.DS↗

arXiv2021

Streaming Hypergraph Partitioning Algorithms on Limited Memory Environments

Many well-known, real-world problems involve dynamic data which describe the relationship among the entities. Hypergraphs are powerful combinatorial structures that are frequently used to model such data. For many of today's data-centric applications, this data is streaming; new items arrive continuously, and the data grows with time. With paradigms such as Internet of Things and Edge Computing, such applications become more natural and more practical. In this work, we assume a streaming model where the data is modeled as a hypergraph, which is generated at the edge. This data then partitioned and sent to remote nodes via an algorithm running on a memory-restricted device such as a single board computer. Such a partitioning is usually performed by taking a connectivity metric into account to minimize the communication cost of later analyses that will be performed in a distributed fashion. Although there are many offline tools that can partition static hypergraphs excellently, algorithms for the streaming settings are rare. We analyze a well-known algorithm from the literature and significantly improve its running time by altering its inner data structure. For instance, on a medium-scale hypergraph, the new algorithm reduces the runtime from 17800 seconds to 10 seconds. We then propose sketch- and hash-based algorithms, as well as ones that can leverage extra memory to store a small portion of the data to enable the refinement of partitioning when possible. We experimentally analyze the performance of these algorithms and report their run times, connectivity metric scores, and memory uses on a high-end server and four different single-board computer architectures.

cs.DS↗

arXiv2018

Programming Strategies for Irregular Algorithms on the Emu Chick

The Emu Chick prototype implements migratory memory-side processing in a novel hardware system. Rather than transferring large amounts of data across the system interconnect, the Emu Chick moves lightweight thread contexts to near-memory cores before the beginning of each remote memory read. Previous work has characterized the performance of the Chick prototype in terms of memory bandwidth and programming differences from more typical, non-migratory platforms, but there has not yet been an analysis of algorithms on this system. This work evaluates irregular algorithms that could benefit from the lightweight, memory-side processing of the Chick and demonstrates techniques and optimization strategies for achieving performance in sparse matrix-vector multiply operation (SpMV), breadth-first search (BFS), and graph alignment across up to eight distributed nodes encompassing 64 nodelets in the Chick system. We also define and justify relative metrics to compare prototype FPGA-based hardware with established ASIC architectures. The Chick currently supports up to 68x scaling for graph alignment, 80 MTEPS for BFS on balanced graphs, and 50\% of measured STREAM bandwidth for SpMV.

cs.DC↗