Near-linear Time Algorithm for Approximate Minimum Degree Spanning Trees

Given a graph $G = (V, E)$, we wish to compute a spanning tree whose maximum vertex degree, i.e. tree degree, is as small as possible. Computing the exact optimal solution is known to be NP-hard, since it generalizes the Hamiltonian path problem. For the approximation version of this problem, a $\tilde{O}(mn)$ time algorithm that computes a spanning tree of degree at most $\Delta^* +1$ is previously known [F\"urer \& Raghavachari 1994]; here $\Delta^*$ denotes the minimum tree degree of all the spanning trees. In this paper we give the first near-linear time approximation algorithm for this problem. Specifically speaking, we propose an $\tilde{O}(\frac{1}{\epsilon^7}m)$ time algorithm that computes a spanning tree with tree degree $(1+\epsilon)\Delta^* + O(\frac{1}{\epsilon^2}\log n)$ for any constant $\epsilon \in (0,\frac{1}{6})$. Thus, when $\Delta^*=\omega(\log n)$, we can achieve approximate solutions with constant approximate ratio arbitrarily close to 1 in near-linear time.Comment: 17 page

Exact Algorithms for Maximum Independent Set

We show that the maximum independent set problem (MIS) on an $n$-vertex graph can be solved in $1.1996^nn^{O(1)}$ time and polynomial space, which even is faster than Robson's $1.2109^{n}n^{O(1)}$-time exponential-space algorithm published in 1986. We also obtain improved algorithms for MIS in graphs with maximum degree 6 and 7, which run in time of $1.1893^nn^{O(1)}$ and $1.1970^nn^{O(1)}$, respectively. Our algorithms are obtained by using fast algorithms for MIS in low-degree graphs in a hierarchical way and making a careful analyses on the structure of bounded-degree graphs

An Efficient Local Search for Partial Latin Square Extension Problem

A partial Latin square (PLS) is a partial assignment of n symbols to an nxn grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension problem is an NP-hard problem that asks for a largest extension of a given PLS. In this paper we propose an efficient local search for this problem. We focus on the local search such that the neighborhood is defined by (p,q)-swap, i.e., removing exactly p symbols and then assigning symbols to at most q empty cells. For p in {1,2,3}, our neighborhood search algorithm finds an improved solution or concludes that no such solution exists in O(n^{p+1}) time. We also propose a novel swap operation, Trellis-swap, which is a generalization of (1,q)-swap and (2,q)-swap. Our Trellis-neighborhood search algorithm takes O(n^{3.5}) time to do the same thing. Using these neighborhood search algorithms, we design a prototype iterated local search algorithm and show its effectiveness in comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX and LocalSolver.Comment: 17 pages, 2 figure

TRAVEL WATTLE OF LANDSCAPES, ANTIQUITY AND SPIRITUAL AURA OF SPACE IN TRAVELOGUES BY ZLATKO TOMIČIĆ

U radu se prvi put revalorizira još posve neistražen književni opus tiskanih putopisnih zbirka istaknutoga suvremenog hrvatskog književnika Zlatka Tomičića (Zagreb, 1930. – Zagreb, 2008.). Današnja međunarodna književna produkcija snažno je usmjerena prema oblikovanjima tzv. nefikcionalnih žanrova (memoara, putopisa, autobiografija) pa se prema ulozi reanimiranja misaonoga poklisara realiziraju i Tomičićevi putopisi. Tomičićeva putopisna proza jednim se dijelom promatra u kontekstu njegovih književnih suvremenika i političko-društvene sudbine autora. Međutim rad se u prvome planu usmjerava na književnu analizu i interpretaciju šesnaest putopisnih knjiga te se unutar autorova oblikotvornoga postupka promatraju i njegovi književni utjecaji, književne relacije i refleksivno-filozofski obzori. Bitna konstanta Tomičićeva putopisa jest težnja za polifonijskim i polihistorijskim modelom doživljavanja svijeta. Kao obilježje Tomičićeva umjetničkoga postupka izdvaja se interferencijska realizacija hibridnoga žanra putopisa i stvaranje književnoga pletera, tj. ispreplitanja kozmopolitizma i rodoljublja te povezivanja realističkih zapažanja s konstantom kulturno-duhovne aure opisivanoga prostora.The paper valorizes for the first time a completely unexplored literary opus of published travelogue collections of prominent contemporary Croatian writer Zlatko Tomičić (Zagreb, 1930. – Zagreb, 2008.). Contemporary international literary production is strongly directed to forming of the so called non-fictional genres (memoirs, travelogues, autobiographies), therefore Tomičić’s travelogues are also realized in accordance with the role of reanimating contemplative envoy. Tomičić’s travel prose is partly considered in the context of his literary contemporaries and authors’ political-social destiny. However, the paper is in the first plan directed to literary analysis and interpretation of sixteen travelogues and author’s literary influences, literary relations and reflexive-philosophic visions are considered within his forming procedure. A very important constant of author’s travelogue is aspiration to polyphonic and historic model of life experiencing. The characteristic of Tomičić’s artistic procedure is interferential realization of hybrid travelogue genre and creation of literary wattle i.e. interweaving of cosmopolitism and patriotism and connecting of realistic observations with a constant of cultural-spiritual aura of described space

Hamiltonian Cycle Parameterized by Treedepth in Single Exponential Time and Polynomial Space

For many algorithmic problems on graphs of treewidth $t$, a standard dynamic programming approach gives an algorithm with time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$. It turns out that when one considers the more restrictive parameter treedepth, it is often the case that a variation of this technique can be used to reduce the space complexity to polynomial, while retaining time complexity of the form $2^{\mathcal{O}(d)}\cdot n^{\mathcal{O}(1)}$, where $d$ is the treedepth. This transfer of methodology is, however, far from automatic. For instance, for problems with connectivity constraints, standard dynamic programming techniques give algorithms with time and space complexity $2^{\mathcal{O}(t\log t)}\cdot n^{\mathcal{O}(1)}$ on graphs of treewidth $t$, but it is not clear how to convert them into time-efficient polynomial space algorithms for graphs of low treedepth. Cygan et al. (FOCS'11) introduced the Cut&Count technique and showed that a certain class of problems with connectivity constraints can be solved in time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$. Recently, Hegerfeld and Kratsch (STACS'20) showed that, for some of those problems, the Cut&Count technique can be also applied in the setting of treedepth, and it gives algorithms with running time $2^{\mathcal{O}(d)}\cdot n^{\mathcal{O}(1)}$ and polynomial space usage. However, a number of important problems eluded such a treatment, with the most prominent examples being Hamiltonian Cycle and Longest Path. In this paper we clarify the situation by showing that Hamiltonian Cycle, Hamiltonian Path, Long Cycle, Long Path, and Min Cycle Cover all admit $5^d\cdot n^{\mathcal{O}(1)}$-time and polynomial space algorithms on graphs of treedepth $d$. The algorithms are randomized Monte Carlo with only false negatives.Comment: Presented at WG2020. 20 pages, 2 figure

Collision-Free Network Exploration

International audienceA set of mobile agents is placed at different nodes of a $n$-node network. The agents synchronously move along the network edges in a {\em collision-free} way, i.e., in no round may two agents occupy the same node. In each round, an agent may choose to stay at its currently occupied node or to move to one of its neighbors. An agent has no knowledge of the number and initial positions of other agents. We are looking for the shortest possible time required to complete the collision-free {\em network exploration}, i.e., to reach a configuration in which each agent is guaranteed to have visited all network nodes and has returned to its starting location. We first consider the scenario when each mobile agent knows the map of the network, as well as its own initial position. We establish a connection between the number of rounds required for collision-free exploration and the degree of the minimum-degree spanning tree of the graph. We provide tight (up to a constant factor) lower and upper bounds on the collision-free exploration time in general graphs, and the exact value of this parameter for trees. For our second scenario, in which the network is unknown to the agents, we propose collision-free exploration strategies running in $O(n^2)$ rounds for tree networks and in $O(n^5\log n)$ rounds for general networks

The number of matchings in random graphs

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm to compute this entropy for an arbitrary graph with a girth that diverges in the large size limit, and an analytic result for the entropy in regular and Erdos-Renyi random graph ensembles.Comment: 17 pages, 6 figures, to be published in Journal of Statistical Mechanic

From Loom to Machine: Tibetan Aprons and the Configuration of Place

In this paper I examine how objects become connected to place in complex and contradictory ways. Over the past ten to fi fteen years, rapid transformations in Chinese manufacturing and transportation networks have signifi cantly altered the production, marketing, and consumption of commodities made in the Tibet Autonomous Region and traded in Kalimpong, India, and Kathmandu, Nepal. In an attempt to connect the ethnographic study of material culture with more macrolevel processes of geoeconomic change, I begin the piece with an examination of the changing production, materials, and styles of a very specifi c commodity, the Tibetan women’s apron. I then explore traders’ narratives about the values of handmade, machine-made, wool, and synthetic commodities, arguing that we ought to look beyond dichotomies of ‘old’ versus ‘new’ or ‘authentic’ versus ‘inauthentic’ objects to show in detail how the attachment of commodities to representations of place fi gures importantly in the contemporary study both of globalization and uneven development. Finally, I suggest that Karl Marx’s notion of dead labor is useful in analyzing the recent move towards the revitalization of Tibetan wool for both the domestic Chinese industry and the global tourist industry

Solution processable direct bandgap copper-silver-bismuth iodide photovoltaics : compositional control of dimensionality and optoelectronic properties

Altres ajuts: SRR acknowledges the support from "laCaixa" Foundation (ID 100010434; LCF/BQ/PI20/11760024). Open access publishing facilitated by Monash University, as part of the Wiley - Monash University agreement via the Council of Australian University Librarians.The search for lead-free alternatives to lead-halide perovskite photovoltaic materials resulted in the discovery of copper(I)-silver(I)-bismuth(III) halides exhibiting promising properties for optoelectronic applications. The present work demonstrates a solution-based synthesis of uniform CuAgBiI thin films and scrutinizes the effects of x on the phase composition, dimensionality, optoelectronic properties, and photovoltaic performance. Formation of pure 3D CuAgBiI at x = 1, 2D CuAgBiI at x = 2, and a mix of the two at 1 < x < 2 is demonstrated. Despite lower structural dimensionality, CuAgBiI has broader optical absorption with a direct bandgap of 1.89 ± 0.05 eV, a valence band level at -5.25 eV, improved carrier lifetime, and higher recombination resistance as compared to CuAgBiI. These differences are mirrored in the power conversion efficiencies of the CuAgBiI and CuAgBiI solar cells under 1 sun of 1.01 ± 0.06% and 2.39 ± 0.05%, respectively. The latter value is the highest reported for this class of materials owing to the favorable film morphology provided by the hot-casting method. Future performance improvements might emerge from the optimization of the CuAgBiI layer thickness to match the carrier diffusion length of ≈40-50 nm. Nonencapsulated CuAgBiI solar cells display storage stability over 240 days