Combinatorial algorithms
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<i>AbDesign</i>: An algorithm for combinatorial backbone design guided by natural conformations and sequences Open
Computational design of protein function has made substantial progress, generating new enzymes, binders, inhibitors, and nanomaterials not previously seen in nature. However, the ability to design new protein backbones for function--essent…
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Tropicalizing the Simplex Algorithm Open
We develop a tropical analog of the simplex algorithm for linear programming.\nIn particular, we obtain a combinatorial algorithm to perform one tropical\npivoting step, including the computation of reduced costs, in O(n(m+n)) time,\nwhere…
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Combinatorial Calabi flows on surfaces Open
For triangulated surfaces, we introduce the combinatorial Calabi flow which is an analogue of the smooth Calabi flow. We prove that the solution to the combinatorial Calabi flow exists for all time and converges if and only if the Thurston…
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Algorithms for stable and perturbation-resilient problems Open
We study the notion of stability and perturbation resilience introduced by Bilu and Linial (2010) and Awasthi, Blum, and Sheffet (2012). A combinatorial optimization problem is α-stable or α-perturbation-resilient if the optimal solution d…
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Combinatorial Flows and Their Normalisation Open
This paper introduces combinatorial flows that generalize combinatorial proofs such that they also include cut and substitution as methods of proof compression. We show a normalization procedure for combinatorial flows, and how syntactic p…
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An Improved Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market Open
We present an improved combinatorial algorithm for the computation of equilibrium prices in the linear Arrow-Debreu model. For a market with n agents and integral utilities bounded by U, the algorithm runs in O(n7 log3(nU)) time. This impr…
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An Improved Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market Open
We present an improved combinatorial algorithm for the computation of equilibrium prices in the linear Arrow-Debreu model. For a market with $n$ agents and integral utilities bounded by $U$, the algorithm runs in $O(n^7 \log^3 (nU))$ time.…
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Combinatorial Proofs of Addition Formulas Open
In this paper we give a combinatorial proof of an addition formula for weighted partial Motzkin paths. The addition formula allows us to determine the $LDU$ decomposition of a Hankel matrix of the polynomial sequence defined by weighted pa…
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Combinatorial relaxation algorithm for the entire sequence of the maximum degree of minors in mixed polynomial matrices Open
Iwata-Takamatsu (2013) showed that the maximum degree of minors in mixed polynomial matrices for a specified order can be computed by combinatorial relaxation type algorithm. In this letter, based on their algorithm, we propose an efficien…
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Predicting structures of large protein assemblies using combinatorial assembly algorithm and AlphaFold2 Open
Deep learning models, such as AlphaFold2 and RosettaFold, enable high-accuracy protein structure prediction. However, large protein complexes are still challenging to predict due to their size and the complexity of interactions between mul…
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Bounds and algorithms for graph trusses Open
The $k$-truss, introduced by Cohen (2005), is a graph where every edge is incident to at least $k$ triangles. This is a relaxation of the clique. It has proved to be a useful tool in identifying cohesive subnetworks in a variety of real-wo…
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Pandora's Problem with Combinatorial Cost Open
Pandora’s problem is a fundamental model in economics that studies optimal search strategies under costly inspection. In this paper we initiate the study of Pandora’s problem with combinatorial costs, capturing many real-life scenarios whe…
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Combinatorial Ski Rental and Online Bipartite Matching Open
We consider a combinatorial variant of the classical ski rental problem --- which we call combinatorial ski rental --- where multiple resources are available to purchase and to rent, and are demanded online. Moreover, the costs of purchasi…
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Evaluating Typical Algorithms of Combinatorial Optimization to Solve Continuous-Time Based Scheduling Problem Open
We consider one approach to formalize the Resource-Constrained Project Scheduling Problem (RCPSP) in terms of combinatorial optimization theory. The transformation of the original problem into combinatorial setting is based on interpreting…
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Ensemble Algorithms and Analytic Combinatorics in RNA Bioinformatics and Beyond Open
La bioinformatique prédictive représente un domaine majeur d'application pour les techniques d'optimisation combinatoire. Très souvent, une perspective ensembliste, ne se limitant pas à une solution optimale mais considèrant l'espace des s…
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Competitive Equilibrium with Chores: Combinatorial Algorithm and Hardness Open
We study the computational complexity of finding a competitive equilibrium (CE) with chores when agents have linear preferences. CE is one of the most preferred mechanisms for allocating a set of items among agents. CE with equal incomes (…
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Combinatorial Exploration: An algorithmic framework for enumeration Open
Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions. We describe how it works an…
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Diversity in Combinatorial Optimization Open
When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good…
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Maximum Bipartite Matching in 𝑛 <sup>2+𝑜(1)</sup> Time via a Combinatorial Algorithm Open
Maximum bipartite matching (MBM) is a fundamental problem in combinatorial optimization with a long and rich history. A classic result of Hopcroft and Karp (1973) provides an O(m √n)-time algorithm for the problem, where n and m are the nu…
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Saturated Fully Leafed Tree-Like Polyforms and Polycubes Open
We present recursive formulas giving the maximal number of leaves in tree-like polyforms living in two-dimensional regular lattices and in tree-like polycubes in the three-dimensional cubic lattice. We call these tree-like polyforms and po…
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Classical and Quantum Algorithms for USO Recognition Open
Unique Sink Orientations (USOs) are orientations of the hypercube graph capable of encoding many optimization problems, such as linear programming. When a USO is given in implicit form as an oracle, the USO recognition problem aims to dist…
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RosettaAMRLD: A Reaction-Driven Approach for Structure-Based Drug Design from Combinatorial Libraries with Monte Carlo Metropolis Algorithms Open
The Rosetta automated Monte Carlo reaction-based ligand design (RosettaAMRLD) integrates a Monte Carlo Metropolis (MCM) algorithm and reaction-driven molecule proposal to enhance structure-based de novo drug discovery. By leveraging combin…
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Using Periodicity Properties to Generate the Combinatorial Configurations Open
Identifying patterns of the ordering of a certain combinatorial set allows to develop of simple procedures for its generation for an arbitrary value and to strictly prove that this set contains all non-identical combinatorial configuration…
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Negative-Weight Single-Source Shortest Paths in Near-linear Time Open
We present a randomized algorithm that computes single-source shortest paths (SSSP) in $O(m\log^8(n)\log W)$ time when edge weights are integral and can be negative. This essentially resolves the classic negative-weight SSSP problem. The p…
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Combinatorial Algorithms for Submodular Function Minimization and Related Problems Open
Submodular functions are common in combinatorics; examples include the cut capacity function of a graph and the rank function of a matroid. The submodular function minimization problem generalizes the classical minimum cut problem and also…
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Finding Even Cycles Faster via Capped k-Walks Open
In this paper, we consider the problem of finding a cycle of length $2k$ (a $C_{2k}$) in an undirected graph $G$ with $n$ nodes and $m$ edges for constant $k\ge2$. A classic result by Bondy and Simonovits [J.Comb.Th.'74] implies that if $m…
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On Combinatorial Models for Affine Crystals Open
The tableau model for Kirillov-Reshetikhin (KR) crystals, which are finite dimensional crystals corresponding to certain affine Lie algebras, is commonly used for its ease of crystal operator calculations. However, its simplicity makes qui…
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About an Approach for Constructing Combinatorial Objects Open
The classification of combinatorial objects consists of two sub-problems – construction of objects with given properties and rejection of isomorphic objects. In this paper, we consider generation of combinatorial objects that are uniquely …
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Odd Paths, Cycles and $T$-joins: Connections and Algorithms Open
Minimizing the weight of an edge set satisfying parity constraints is a challenging branch of combinatorial optimization as witnessed by the binary hypergraph chapter of Alexander Schrijver's book ``Combinatorial Optimization" (Chapter 80)…
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Software for enumerative and analytic combinatorics Open
We survey some general-purpose symbolic software packages that implement algorithms from enumerative and analytic combinatorics. Software for the following areas is covered: basic combinatorial objects, symbolic combinatorics, Pólya theory…