arXiv subjects

Dorit S. Hochbaum

Publications and source records attributed to Dorit S. Hochbaum.

At least 19 recordsLinked to original sources

arXiv2026

Diversity-Based Active Learning: An Evaluation of Metric Spaces for Active Learning Selection

With rapid advancement over the last few years, many different methods are now widely used for classification. However, training these models requires substantial labeled data. Active Learning is a potential solution to this problem. Pool-based active learning minimizes costs by querying only the most informative samples from an unlabeled dataset. Diversity-based approaches, on the other hand, attempt to select a representative subset of the data. There are many different objectives for determining the selection process, including exact K-center, exact K-median, and Greedy K-center. In this paper, we will focus on evaluating the performance of Greedy K-center across a variety of metric spaces: the raw feature space, a Linear Discriminant Analysis (LDA) space, and a model-derived probability space (with and without entropy-based weighting). Using Random Forest classifiers as a baseline evaluator, our empirical results on synthetic and real-world datasets demonstrate that mapping unlabeled instances into a predictive probability space and weighting the result by entropy often dominates the other options for active learning selection with Greedy K-center.

cs.LG↗

arXiv2026

A Fast and Effective Method for Euclidean Anticlustering: The Assignment-Based-Anticlustering Algorithm

Anticlustering is an NP-hard combinatorial optimization problem that consists of partitioning a set of objects into equal-sized groups called anticlusters such that the objects in the same anticluster are as dissimilar as possible and thereby representative of the entire set of objects. Here we study the case where the dissimilarity metric is the squared Euclidean distance between the respective feature vectors. Applications of Euclidean anticlustering include social studies, cross-validation, creating mini-batches for stochastic gradient descent, and finding balanced K-cut partitions. In particular, machine-learning applications such as mini-batch generation involve million-scale datasets and very large values of K, making scalable anticlustering algorithms essential. We propose a new algorithm, the Assignment-Based Anticlustering (ABA) algorithm, that scales to instances with millions of objects and hundreds of thousands of anticlusters within seconds to minutes, which is far beyond what existing anticlustering methods can manage. We demonstrate here, via an extensive computational study, that our algorithm outperforms existing anticlustering methods in both solution quality and running time. This is so also for anticlustering with categories. For the related problem of balanced K-cut partitioning, our algorithm is superior to the well-known METIS method. The code of our algorithm is available on GitHub.

cs.LG↗

arXiv2025

Fast and Optimal Incremental Parametric Procedure for the Densest Subgraph Problem: An Experimental Study

The Densest Subgraph Problem (DSP) is widely used to identify community structures and patterns in networks such as bioinformatics and social networks. While solvable in polynomial time, traditional exact algorithms face computational and scalability limitations, leading to the adoption of faster, but non-optimal, heuristic methods. This work presents the first experimental study of the recently devised Incremental Parametric Cut (IPC) algorithm, which is an exact method for DSP and other "monotone ratio problems". Our findings demonstrate that IPC not only overcomes the limitations of previous exact approaches but also substantially outperforms leading state-of-the-art heuristics in both speed and solution quality. IPC's performance is also evaluated here for other "monotone ratio problems" related to conductance, Cheeger constant and normalized cut. For these, our experimental study on large-scale instances demonstrate exceptional computational speed. In particular, comparing IPC with the "fully parametric cut" algorithm, which is the only other efficient known optimization algorithm for such problems, demonstrate the superior performance of IPC. We provide here code and benchmarks, establishing IPC as a fast, scalable, and optimal solution framework for densest subgraph and related monotone ratio problems.

cs.DS↗

arXiv2025

Min cost flow on unit capacity networks and convex cost K-flow are as easy as the assignment problem with All-Min-Cuts algorithm

We explore here surprising links between the time-cost-tradeoff problem and the minimum cost flow problem that lead to fast, strongly polynomial, algorithms for both problems. One of the main results is a new algorithm for the unit capacity min cost flow that matches the complexity of the fastest strongly polynomial algorithm known for the assignment problem. The time cost tradeoff (TCT) problem in project management is to expedite the durations of activities, subject to precedence constraints, in order to achieve a target project completion time at minimum expediting costs, or, to maximize the net benefit from a reward associated with project completion time reduction. Each activity is associated with integer normal duration, minimum duration, and expediting cost per unit reduction in duration. We devise here the {\em all-min-cuts} procedure, which for a given maximum flow, is capable of generating all minimum cuts (equivalent to minimum cost expediting) of equal value very efficiently. Equivalently, the procedure identifies all solutions that reside on the TCT curve between consecutive breakpoints in average $O(m+n \log n)$ time, where $m$ and $n$ are the numbers of arcs and nodes in the network. The all-min-cuts procedure implies faster algorithms for certain TCT problems and for certain min cost flow problem with a significantly different approach from the ones known.

cs.DS↗

arXiv2025

A Fast and Effective Breakpoints Heuristic Algorithm for the Quadratic Knapsack Problem

The Quadratic Knapsack Problem (QKP) involves selecting a subset of elements that maximizes the sum of pairwise and singleton utilities without exceeding a given budget. The pairwise utilities are nonnegative, the singleton utilities may be positive, negative, or zero, and the node costs are nonnegative. We introduce a Breakpoints Algorithm for QKP, named QKBP, which is based on a technique proposed in \cite{Hoc09} for efficiently generating the concave envelope of the solutions to the relaxation of the problem for all values of the budget. Our approach utilizes the fact that breakpoints in the concave envelopes are optimal solutions for their respective budgets. For budgets between breakpoints, a fast greedy heuristic derives high-quality solutions from the optimal solutions of adjacent breakpoints. The QKBP algorithm is a heuristic which is highly scalable due to an efficient parametric cut procedure used to generate the concave envelope. This efficiency is further improved by a newly developed compact problem formulation. Our extensive computational study on both existing and new benchmark instances, with up to 10,000 elements, shows that while some leading algorithms perform well on a few instances, QKBP consistently delivers high-quality solutions regardless of instance size, density, or budget. Moreover, QKBP achieves these results in significantly faster running times than all leading algorithms. The source code of the QKBP algorithm, the benchmark instances, and the detailed results are publicly available on GitHub.

math.OC↗

arXiv2025

The Strong Maximum Circulation Algorithm: A New Method for Aggregating Preference Rankings

We present a new optimization-based method for aggregating preferences in settings where each voter expresses preferences over pairs of alternatives. Our approach to identifying a consensus partial order is motivated by the observation that collections of votes that form a cycle can be treated as collective ties. Our approach then removes unions of cycles of votes, or circulations, from the vote graph and determines aggregate preferences from the remainder. Specifically, we study the removal of maximal circulations attained by any union of cycles the removal of which leaves an acyclic graph. We introduce the strong maximum circulation, the removal of which guarantees a unique outcome in terms of the induced partial order, called the strong partial order. The strong maximum circulation also satisfies strong complementary slackness conditions, and is shown to be solved efficiently as a network flow problem. We further establish the relationship between the dual of the maximum circulation problem and Kemeny's method, a popular optimization-based approach for preference aggregation. We also show that identifying a minimum maximal circulation -- i.e., a maximal circulation containing the smallest number of votes -- is an NP-hard problem. Further an instance of the minimum maximal circulation may have multiple optimal solutions whose removal results in conflicting partial orders.

cs.SI↗

arXiv2024

An algorithm for clustering with confidence-based must-link and cannot-link constraints

We study here the semi-supervised $k$-clustering problem where information is available on whether pairs of objects are in the same or in different clusters. This information is either available with certainty or with a limited level of confidence. We introduce the PCCC (Pairwise-Confidence-Constraints-Clustering) algorithm, which iteratively assigns objects to clusters while accounting for the information provided on the pairs of objects. Our algorithm uses integer programming for the assignment of objects which allows to include relationships as hard constraints that are guaranteed to be satisfied or as soft constraints that can be violated subject to a penalty. This flexibility distinguishes our algorithm from the state-of-the-art in which all pairwise constraints are either considered hard, or all are considered soft. We developed an enhanced multi-start approach and a model-size reduction technique for the integer program that contributes to the effectiveness and the efficiency of the algorithm. Unlike existing algorithms, our algorithm scales to large-scale instances with up to 60,000 objects, 100 clusters, and millions of cannot-link constraints (which are the most challenging constraints to incorporate). We compare the PCCC algorithm with state-of-the-art approaches in an extensive computational study. Even though the PCCC algorithm is more general than the state-of-the-art approaches in its applicability, it outperforms the state-of-the-art approaches on instances with all hard or all soft constraints both in terms of runtime and various metrics of solution quality. The code of the PCCC algorithm is publicly available on GitHub.

cs.LG↗

arXiv2024

Binary weights spanning trees and the $k$-red spanning tree problem in linear time

We address here spanning tree problems on a graph with binary edge weights. For a general weighted graph the minimum spanning tree is solved in super-linear running time, even when the edges of the graph are pre-sorted. A related problem, of finding a spanning tree with a pre-specified sum of weights, is NP-hard. In contrast, for a graph with binary weights associated with the edges, it is shown that the minimum spanning tree and finding a spanning tree with a given total sum, are solvable in linear time with simple algorithms.

cs.DS↗

arXiv2021

A Graph-Theoretic Approach for Spatial Filtering and Its Impact on Mixed-type Spatial Pattern Recognition in Wafer Bin Maps

Statistical quality control in semiconductor manufacturing hinges on effective diagnostics of wafer bin maps, wherein a key challenge is to detect how defective chips tend to spatially cluster on a wafer--a problem known as spatial pattern recognition. Recently, there has been a growing interest in mixed-type spatial pattern recognition--when multiple defect patterns, of different shapes, co-exist on the same wafer. Mixed-type spatial pattern recognition entails two central tasks: (1) spatial filtering, to distinguish systematic patterns from random noises; and (2) spatial clustering, to group filtered patterns into distinct defect types. Observing that spatial filtering is instrumental to high-quality mixed-type pattern recognition, we propose to use a graph-theoretic method, called adjacency-clustering, which leverages spatial dependence among adjacent defective chips to effectively filter the raw wafer maps. Tested on real-world data and compared against a state-of the-art approach, our proposed method achieves at least 46% gain in terms of internal cluster validation quality (i.e., validation without external class labels), and about ~5% gain in terms of Normalized Mutual Information--an external cluster validation metric based on external class labels. Interestingly, the margin of improvement appears to be a function of the pattern complexity, with larger gains achieved for more complex-shaped patterns.

stat.AP↗

arXiv2021

Joint aggregation of cardinal and ordinal evaluations with an application to a student paper competition

An important problem in decision theory concerns the aggregation of individual rankings/ratings into a collective evaluation. We illustrate a new aggregation method in the context of the 2007 MSOM's student paper competition. The aggregation problem in this competition poses two challenges. Firstly, each paper was reviewed only by a very small fraction of the judges; thus the aggregate evaluation is highly sensitive to the subjective scales chosen by the judges. Secondly, the judges provided both cardinal and ordinal evaluations (ratings and rankings) of the papers they reviewed. The contribution here is a new robust methodology that jointly aggregates ordinal and cardinal evaluations into a collective evaluation. This methodology is particularly suitable in cases of incomplete evaluations -- i.e., when the individuals evaluate only a strict subset of the objects. This approach is potentially useful in managerial decision making problems by a committee selecting projects from a large set or capital budgeting involving multiple priorities.

cs.AI↗

arXiv2020

A Fully Polynomial Time Approximation Scheme for the Replenishment Storage Problem

The Replenishment Storage problem (RSP) is to minimize the storage capacity requirement for a deterministic demand, multi-item inventory system where each item has a given reorder size and cycle length. The reorders can only take place at integer time units within the cycle. This problem was shown to be weakly NP-hard for constant joint cycle length (the least common multiple of the lengths of all individual cycles). When all items have the same constant cycle length, there exists a Fully Polynomial Time Approximation Scheme (FPTAS), but no FPTAS has been known for the case when the individual cycles are different. Here we devise the first known FPTAS for the RSP with different individual cycles and constant joint cycle length.

cs.DS↗

arXiv2020

Algorithms and Complexity for Variants of Covariates Fine Balance

We study here several variants of the covariates fine balance problem where we generalize some of these problems and introduce a number of others. We present here a comprehensive complexity study of the covariates problems providing polynomial time algorithms, or a proof of NP-hardness. The polynomial time algorithms described are mostly combinatorial and rely on network flow techniques. In addition we present several fixed-parameter tractable results for problems where the number of covariates and the number of levels of each covariate are seen as a parameter.

cs.DS↗

arXiv2020

Network Flow Methods for the Minimum Covariates Imbalance Problem

The problem of balancing covariates arises in observational studies where one is given a group of control samples and another group, disjoint from the control group, of treatment samples. Each sample, in either group, has several observed nominal covariates. The values, or categories, of each covariate partition the treatment and control samples to a number of subsets referred to as \textit{levels} where the samples at every level share the same covariate value. We address here a problem of selecting a subset of the control group so as to balance, to the best extent possible, the sizes of the levels between the treatment group and the selected subset of control group, the min-imbalance problem. It is proved here that the min-imbalance problem, on two covariates, is solved efficiently with network flow techniques. We present an integer programming formulation of the problem where the constraint matrix is totally unimodular, implying that the linear programming relaxation to the problem has all basic solutions, and in particular the optimal solution, integral. This integer programming formulation is linked to a minimum cost network flow problem which is solvable in $O(n\cdot (n' + n\log n))$ steps, for $n$ the size of the treatment group and $n'$ the size of the control group. A more efficient algorithm is further devised based on an alternative, maximum flow, formulation of the two-covariate min-imbalance problem, that runs in $O(n'^{3/2}\log^2n)$ steps.

cs.DS↗

arXiv2020

The Max-Cut Decision Tree: Improving on the Accuracy and Running Time of Decision Trees

Decision trees are a widely used method for classification, both by themselves and as the building blocks of multiple different ensemble learning methods. The Max-Cut decision tree involves novel modifications to a standard, baseline model of classification decision tree construction, precisely CART Gini. One modification involves an alternative splitting metric, maximum cut, based on maximizing the distance between all pairs of observations belonging to separate classes and separate sides of the threshold value. The other modification is to select the decision feature from a linear combination of the input features constructed using Principal Component Analysis (PCA) locally at each node. Our experiments show that this node-based localized PCA with the novel splitting modification can dramatically improve classification, while also significantly decreasing computational time compared to the baseline decision tree. Moreover, our results are most significant when evaluated on data sets with higher dimensions, or more classes; which, for the example data set CIFAR-100, enable a 49% improvement in accuracy while reducing CPU time by 94%. These introduced modifications dramatically advance the capabilities of decision trees for difficult classification tasks.

cs.LG↗

arXiv2018

DISPATCH: An Optimally-Competitive Algorithm for Maximum Online Perfect Bipartite Matching with i.i.d. Arrivals

This work presents an optimally-competitive algorithm for the problem of maximum weighted online perfect bipartite matching with i.i.d. arrivals. In this problem, we are given a known set of workers, a distribution over job types, and non-negative utility weights for each pair of worker and job types. At each time step, a job is drawn i.i.d. from the distribution over job types. Upon arrival, the job must be irrevocably assigned to a worker and cannot be dropped. The goal is to maximize the expected sum of utilities after all jobs are assigned. We introduce DISPATCH, a 0.5-competitive, randomized algorithm. We also prove that 0.5-competitive is the best possible. DISPATCH first selects a "preferred worker" and assigns the job to this worker if it is available. The preferred worker is determined based on an optimal solution to a fractional transportation problem. If the preferred worker is not available, DISPATCH randomly selects a worker from the available workers. We show that DISPATCH maintains a uniform distribution over the workers even when the distribution over the job types is non-uniform.

cs.DS↗

arXiv2018

Algorithms and Complexity of Range Clustering

We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called clusters or classes, consisting of similar objects so that different clusters are as dissimilar as possible. We propose a number of objective functions that employ the range of the clusters as part of the objective function. Several of the proposed objectives mimic objectives based on sums of similarities. These objective functions are motivated by image segmentation problems, where the diameter, or range of values associated with objects in each cluster, should be small. It is demonstrated that range-based problems are in general easier, in terms of their complexity, than the analogous similarity-sum problems. Several of the problems we present could therefore be viable alternatives to existing clustering problems which are NP-hard, offering the advantage of efficient algorithms.

cs.DS↗

arXiv2018

Efficient algorithms to discover alterations with complementary functional association in cancer

Recent large cancer studies have measured somatic alterations in an unprecedented number of tumours. These large datasets allow the identification of cancer-related sets of genetic alterations by identifying relevant combinatorial patterns. Among such patterns, mutual exclusivity has been employed by several recent methods that have shown its effectivenes in characterizing gene sets associated to cancer. Mutual exclusivity arises because of the complementarity, at the functional level, of alterations in genes which are part of a group (e.g., a pathway) performing a given function. The availability of quantitative target profiles, from genetic perturbations or from clinical phenotypes, provides additional information that can be leveraged to improve the identification of cancer related gene sets by discovering groups with complementary functional associations with such targets. In this work we study the problem of finding groups of mutually exclusive alterations associated with a quantitative (functional) target. We propose a combinatorial formulation for the problem, and prove that the associated computation problem is computationally hard. We design two algorithms to solve the problem and implement them in our tool UNCOVER. We provide analytic evidence of the effectiveness of UNCOVER in finding high-quality solutions and show experimentally that UNCOVER finds sets of alterations significantly associated with functional targets in a variety of scenarios. In addition, our algorithms are much faster than the state-of-the-art, allowing the analysis of large datasets of thousands of target profiles from cancer cell lines. We show that on one such dataset from project Achilles our methods identify several significant gene sets with complementary functional associations with targets.

q-bio.QM↗

arXiv2017

Submodular problems - approximations and algorithms

We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables appear with opposite sign coefficients) then the problems of submodular minimization or supermodular maximization are polynomial time solvable. The key idea is to link these problems to a submodular s,t-cut problem defined here. This framework includes the problems: SM-vertex cover; SM-2SAT; SM-min satisfiability; SM-edge deletion for clique, SM-node deletion for biclique and others. We also introduce here the submodular closure problem and and show that it is solvable in polynomial time and equivalent to the submodular cut problem. All the results are extendible to multi-sets where each element of a set may appear with a multiplicity greater than 1. For all these NP-hard problems 2-approximations are the best possible in the sense that a better approximation factor cannot be achieved in polynomial time unless NP=P. The mechanism creates a relaxed "monotone" problem, solved as a submodular closure problem, the solution to which is mapped to a half integral super-optimal solution to the original problem. That half-integral solution has the persistency property meaning that integer valued variables retain their value in an optimal solution. This permits to delete the integer valued variables, and restrict the search of an optimal solution to the smaller set of remaining variables.

cs.DM↗